CBE 320 Past Quizzes
For a monatomic gas at low density, its thermal conductivity has the same (temperature)1/2 dependence as its viscosity; this statement is true / false
true
As a start-up company, you and your marketing partner are exploring an idea to disrupt the business of chocolate-dipped cones (see image); a "deep-dip process" would allow more fluid chocolate to coat the cone. Before testing the process with expensive chocolate and specialized equipment, you wish to develop a model for the cost of chocolate per cone by the deep-dip process. What coordinate system would you choose to model the flow from the surface of the cone after it has been dipped in fluid chocolate? Briefly explain your reasoning.
Choose spherical coordinates. The surface on which flow occurs is readily defined as a surface of constant angle theta (in spherical coordinates); see also BSLK Fig. 1.2-2(b) bottom/right figure.
Write an integral expression for the z-component of molecular force exerted by a flowing fluid on the end of a cylinder oriented in the positive-z direction. The cylinder is aligned with the z-axis and centered at the origin. You may assume the cylinder has radius R and total length L.
Ffs,z=−τzz+p()0R∫02π∫z=(L/2)rdrdθ
Flow through a circular tube versus flow through an annulus. If one compares the derivation of velocity distributions for flows in these two geometries one finds: a) that their shell balances are similar or identical. b) that differences between their shell balances give rise to different differential equations for their shear stress distributions. c) none
a
Equations of change and other mathematical expressions play a central role in transport phenomena to describe how parameters like fluid velocity, material temperature, or molar concentration vary with spatial position over time. 1) In its most general formulation, the equation of continuity (Appendix B.4, BSLK) for a fluid is expressed in terms of its density (a scalar) as well as its velocity (a vector). Since the equation of continuity describes the time rate of change of the fluid density at a fixed point in space it is a a) scalar equation b) vector equation c) tensor equation
a
Given the dimensions of length(L), mass(M), and time(T), we know that velocity has dimensions of length per time (L/T). Therefore, shear stress has dimensions of (select the best answer): a) M/(LT^2) b) M/(LT) c) 1/T d) M/T e) L/T^2
a
5) In its most general formulation, the macroscopic mechanical energy balance (7.4-1, page 193, BSLK) is a a) scalar equation b) vector equation c) tensor equation
a
At a liquid-liquid interfacial plane of constant x, we generally have: a) Tangential velocity components (vyvy and vzvz ) are continuous through the interface ('no-slip condition') b) Tangential velocity components (vyvy and vzvz) are zero at the interface c) Stress-tensor components (τxyτxy and τxzτxz ) are zero d) Kinematic viscosities on both sides of the interface are equal
a
At steady state the temperature profiles in a laminated system appear as in the figure. Which material has the higher thermal conductivity? Quiz 10 problem 3 image a) material 1 b) material 2
a
Consider slow radial flow between two parallel flat disks as shown in the figure. If one assumes steady-state flow behavior where flows in the radial direction depend on r and z, while flows in theta and z directions can be neglected, then the continuity equation enables one to show explicitly how the radial velocity depends on Quiz 6 problem 4 image a) r, the radial coordinate b) z, the axial coordinate c) theta(θ ), the angular coordinate d) p, the pressure at different radial positions e) none
a
Consider slow radial flow between two porous coaxial cylinders as shown in the figure (top view). If one assumes steady-state flow of a Newtonian fluid where flows in the radial direction depend on r, while flows in theta and z directions can be neglected, then the continuity equation enables one to show explicitly how the radial velocity depends on image quiz 6 problem 5 a) r, the radial coordinate b) z, the axial coordinate c) theta(θ ), the angular coordinate d) p, the pressure at different radial positions e) none
a
Consider the heating of fluid as it is flows between various unit operations in the chemical process industries. The unit operation or process that is most commonly employed to carry out such fluid heating is: a) the heat exchanger b) heating tape wrapped around the outer surface of the tube c) resistive heating by passing an electrical current through the tube d) viscous dissipation
a
Creeping fluid flow about a sphere (e.g., particle, aerosol droplet, or bubble). As a sphere in a fluid rises or falls, subject to the force of gravity, its motion depends on both buoyant and drag forces. 7) The buoyant force that a sphere in a fluid experiences depends on: a) the density of the fluid b) the density of the sphere c) the velocity of the sphere relative to the fluid d) all of the above e) none of the above
a
In Cartesian coordinates, one may imagine a surface that satisfies the following relationships: y = 20x and z = [-∞ ,∞ ] In words, this surface is defined by a linear relationship between y and x, and all real number values of z from minus infinity to plus infinity. This surface is best described as a) a surface that is overall closer to the y-z plane than the x-z plane b) a surface that are parallel to the x-y plane for any value of z c) a surface that is overall closer to the x-z plane than the y-z plane d) a surface that is overall closer to the x-y plane than the x-z plane e) none
a
In a cylindrical coordinate system, where any point in space may be defined by specifying its coordinates (r,θ, z), consider a surface of fixed radius (r = R). A differential area element on this surface may be written as: a) R(dθ)(dz) b) R(dz) c) 2π R(dz) d) (dr)(dθ)(dz) e) 2π (dr)(dz) f) none
a
In general, as a gas is heated, how do its properties of momentum, heat, and mass transport change? a) Viscosity increases, thermal conductivity increases, and diffusivity increases b) Viscosity decreases, thermal conductivity increases, and diffusivity increases c) Viscosity increases, thermal conductivity decreases, and diffusivity increases d) Viscosity increases, thermal conductivity increases, and diffusivity decreases
a
In the absence of fluid flows, the flux of energy as heat is driven by: (choose the best answer): a) conduction b) natural (free) convection c) pressure - driven convection d) friction factors e) none
a
In times of COVID-19, a heating filtration system may be supplemented with filters to remove contaminants from water. In addition to removing contaminants, filters create barriers to water flow that can require higher energy costs to move large volumes of water through the filter. With these considerations in mind, it would be better to filter the water (select the better answer): a) after it has been heated b) before it has been heated
a
Introduction. Consider two immiscible (non-mixing) Newtonian liquids confined to the space between two parallel flat plates as shown; the lower plate is stationary and the upper plate moves in the positive x-direction with constant velocity V0, and the gravitational force, g, acts in the negative y direction as shown. Assume each liquid occupies an equivalent depth, and liquid 1 is less dense than liquid 2. Consider three cases for steady velocity distributions of the liquids 3) If liquid 2 has a higher viscosity than liquid 1, then we expect the flow velocity of a) steeper slope in region 1 b) steeper slope in region 2 c) equal slopes in region 1 and 2
a
Newton's Law of Viscosity in Cartesian(rectangular) coordinates may be expressed as follows (select the best answer): a) τxy=−μdvy/dx b) τxy=μdvx/dy c) τxy=μdvy/dy d) τxy=−μdvy/dz
a
Shear rate is an example of a: a) scalar b) vector c) tensor
a
The integral expression Ffs,z=−∫2π0∫R0(τzz+p)∣z=(L2)rdrdθ represents the force of a fluid acting on (choose the best answer) a) the flat disc-shaped surface at the end of a cylinder b) the curved outer surface of a cylindrical tube c) the curved inner surface of a cylindrical tube d) the curved surface of the upper half of a sphere with radius R centered at the origin
a
The process of free (or natural) convection arises in fluid systems where flow is driven by the dependence of: a) fluid density on temperature b) fluid viscosity on temperature c) fluid viscosity on pressure d) none
a
The velocity distribution of a falling film is useful because it can be used to determine: a) maximum fluid velocity b) average fluid velocity c) volumetric flow rate d) mass flow rate e) the z-direction force of the fluid acting on the stationary surface f) all g) none
all
Air is pumped into water (a Newtonian fluid) and the resulting bubbles transfer oxygen to the water. We would like to estimate the force on a bubble as it rises through the water. For simplicity, assume the bubble is spherical with constant radius R. Indicate which of the following equations provides the best description for the overall shear force by the fluid on the bubble as it rises. a) ∫02π∫0πτrϕ∣r=RR2sinθdθdϕ b) ∫02π∫0π−τrθ∣r=RR2sinθdθdϕ
b
Cone-and-plate viscometry is used to measure the viscosity of a liquid based on the torque needed to maintain rotation of a solid cone at a constant angular velocity; the apex of the cone just contacts the plate, and the liquid is placed in the gap between the cone and plate, as shown in the figure. Choose one option below to complete the true statement. For sufficiently small values of the angle between the cone and the plate (ψ0 ),__________________ can be approximated by a velocity distribution in Cartesian coordinates, Vx(y), which increases linearly with the distance from the lower stationary plate Quiz 4 problem 7 image a) the angular velocity in cylindrical coordinates (Vθ ) b) the angular velocity in spherical coordinates (Vϕ ) c) the radial velocity in cylindrical coordinates (Vr ) d) the radial velocity in spherical coordinates (Vr )
b
Consider a Newtonian fluid between two parallel flat plates as shown; the lower plate is stationary and the upper plate moves in the positive x-direction with velocity V0. Two versions are shown of the same setup; they only differ by the origin of the coordinate system, which is aligned with either the lower plate (left) or the upper plate (right). Which statement below best describes these two systems? Quiz 2 problem 5 image a) Since the two versions are physically identical, both versions will have the same mathematical function for the velocity distribution of interest, vx(y). b) The two versions are physically identical, but the coordinate systems are different, so the two versions will have different velocity distributions of interest, vx(y). c) The two versions are physically identical, but the coordinate systems are different, so the two versions will have the same values for the relevant shear stress component, τyxτyx . d) Both (a) and (c) above are true. e) Both (b) and (c) above are true. f) none are true
b
Consider an equation for the force acting in the z-direction and its dependence on a molecular momentum flux, π . Fz=[]π The term in the brackets [ ] should have dimensions of: a) length b) area c) volume d) pressure e) density f) none - dimensionless
b
Consider the relationship for heat-transfer coefficients for fully developed flow in smooth tubes, as shown in the figure. The flow regimes that are most often avoided in engineering design are: quiz 12 problem 2 image a) Re<2100 b) 2100<Re<8000 c) Re>20000
b
If a potato at room temperature is suddenly submerged into a pot of boiling water, the surface of the potato will initially heat up and a front of energy as heat will gradually penetrate toward the center of the potato. The depth of penetration of the heat front will be proportional to (or scale with) the a) elapsed time b) elapsed time ^1/2 c) elapsed time ^1/4 d) none
b
If an increase in the fluid flow rate in question (2) causes a transition from laminar to turbulent flow, then the average fluid temperature and mixing-cup temperature will: The heating of a fluid of known temperature as it flows through a single heated tube. a) be identical b) become more similar to each other c) become more different from each other
b
If you wish to design a continuous-flow system that supplies heated water at a desired (controllable) temperature, then your calculations based on question (2) would need to estimate the dependence on tube length of the: The heating of a fluid of known temperature as it flows through a single heated tube. a) average fluid temperature b) mixing - cup temperature
b
In its most general formulation, Fourier's Law of Heat Conduction (Appendix B.2, BSLK) describes for 3-dimensional time-dependent flux of energy as heat and its dependence on temperature gradients; it is a a) scalar equation b) vector equation c) tensor equation
b
In its most general formulation, the equation of motion (Appendix B.5, BSLK) for a fluid describes the conservation of momentum; it is a a) scalar equation b) vector equation c) tensor equation
b
In order to calculate power requirements to pump a fluid through a piping system one needs to estimate energy losses due to friction. The magnitude of such losses, which are associated with flow through conduits as well as fittings and valves, share the feature that they are (circle the best answer): a) independent of the average fluid velocity b) dependent on the average fluid velocity c) negligible for turbulent flow systems d) negligible for laminar flow systems e) none
b
In spherical coordinates, one may imagine an object defined by θ=[0,π],r=[0,R],ϕ=π/9 In words, this object is defined by an angle theta that spans from 0 to π , a radial dimension that spans from the origin to R (a positive real number), and constant value for the angle phi. This object is best described as a) a sphere of radius R, centered at the origin b) a disc that intersects the z-axis and has area πR^2/2 c) the outer surface of a cylinder with radius R and height of (R)cos(π/9) d) cone
b
In times of COVID-19, heating, ventilation, and air conditioning (HVAC) systems may be supplemented with filters to remove contaminants from the air. In addition to removing contaminants, filters create barriers to air flow that can require higher energy costs to move large volumes of air through the filter. With these considerations in mind, it would be better to filter the air (select the better answer): a) after it has been heated b) before it has been heated
b
Introduction. Consider two immiscible (non-mixing) Newtonian liquids confined to the space between two parallel flat plates as shown; the lower plate is stationary and the upper plate moves in the positive x-direction with constant velocity V0, and the gravitational force, g, acts in the negative y direction as shown. Assume each liquid occupies an equivalent depth, and liquid 1 is less dense than liquid 2. Consider three cases for steady velocity distributions of the liquids 2) If liquid 1 has a higher viscosity than liquid 2, then we expect the flow velocity of a) steeper slope in region 1 b) steeper slope in region 2 c) equal slopes in region 1 and 2
b
One often describes steady turbulent flow of a Newtonian fluid in a tube as having 'plug flow' behavior. This is consistent with the observation that (<v>/vmax), the ratio of the average fluid velocity to the maximum fluid velocity, is: a) closer to unity for laminar flow than it is for turbulent flow b) closer to unity for turbulent flow than it is for laminar flow c) described by a parabolic profile for both laminar and turbulent flow d) both b and c e) none
b
The behavior of the transient velocity profiles in Question 1 would depend on: Quiz 13 Problem 2 referencing problem 1 a) the densities of the fluid and the sphere b) the density and viscosity of the fluid c) the thermal conductivity of the sphere and the viscosity of the fluid d) the density of the sphere and the viscosity of the fluid
b
The instantaneous velocity, v(t), can be written as the sum of the time-smoothed velocity and the velocity fluctuation: v(t)=v¯+v′(t) When this expression is substituted into the equation of motion and the resulting equation is time-smoothed and simplified, new terms called Reynolds stresses arise owing to: a) time-smoothing of terms that are linear (or proportional to) v'(t) b) time-smoothing of terms that are quadratic in v'(t) (or proportional to [v'(t)]^2 c) time-smoothing of externally applied forces such as gravity
b
The similarity solution in question (9) reduces the original PDE to an ODE that can be solved with: a) one boundary condition b) two boundary conditions c) three boundary conditions
b
The ventilation ducts in a building have square cross-sections of width (W) and cross-sectional area W2. Hence, the mean hydraulic radius for such ducts is given by (circle one): a) w/2 b) w/4 c) 2w/π d) w/√π e) w/√2
b
Transient momentum transfer. A hollow magnetic sphere of radius 2 cm is submerged in a large vat of water (a Newtonian fluid) with constant fluid properties, as shown in the figure. The sphere has the same overall density as the water, so it neither settles nor rises relative to the downward gravitational force. Assume the relevant coordinate system has its origin at the center of the sphere. At 9:30am, an external electric field is imposed such that the sphere immediately starts spinning in the positive-phi direction at a constant angular velocity, Vϕ . The differential equation that best describes the transient velocity distribution of the water is given by: Quiz 13 problem 1 image and solution options a) b) c) d)
b
Turbulent flow in a tube is characterized by rapid fluctuations in velocity. One may express the instantaneous z-component of velocity as follows: vz=vz¯¯¯¯¯¯+v′zvz=vz¯+vz′ where the overbar indicates a time-smoothed value and the prime indicates the time-dependent fluctuation. Which of the following expressions is in general non-zero? (choose the best answer) Quiz 6 problem 10 - formulas a) b) c) d) none
b
Which two terms would be most likely negligible compared to the magnitude of the remaining terms? Quiz 9 problem 5 image a) terms 1 and 2 b) terms 1 and 3 c) terms 1 and 4 d) terms 2 and 3 d) terms 2 and 4 d) terms 3 and 4
b
2) Consider the same setup as in Problem 1, above, however both plates are stationary. The fluid between the plates still flows to the right (positive x-direction) owing to a difference in pressure, p(x=0) is greater than p(x=L), where the pressure of the fluid at the origin is higher than the pressure of the fluid at some location L length units from the origin, measured in the direction of x. Here, a distribution of fluid velocity is established such that: a) both the velocity and shear stress distribution are linear functions of y. b) both the velocity and shear stress distribution are parabolic functions of y. c) the velocity distribution is parabolic with respect to y, and the shear stress distribution is linear with respect to y. d) the velocity distribution is linear with respect to y, and the shear stress distribution is parabolic with respect to y. e) none
c
A centrifugal pump is capable of producing flows of different magnitudes while keeping the pressure at the pump exit essentially constant. Such a pump is installed at one end of a pipe and a valve is installed at the other end, as shown in the figure. Initially the valve is partially opened. When the valve is opened wider so that the flow rate increases, it is also found that (circle one): Quiz 8 problem 8 - also solution options a) b) c) d)
c
At a liquid-gas interfacial plane of constant x, we generally have: a) Tangential velocity components (vy and vz ) are continuous through the interface ('no-slip condition') b) Tangential velocity components (vy and vz ) are zero at the interface c) Stress-tensor components ( τxy and τxz ) are zero d) Momentum fluxes in the x-direction are non-zero
c
Consider the heating of a fluid of known temperature as it flows through a single heated tube. It is feasible to develop an approximate analytical solution for the temperature of the fluid exiting tube if one assumes: a) the outer surface temperature of the tube depends on a constant heat transfer coefficient b) the outer-wall temperature of the tube is constant c) the heat flux from the tube wall to the fluid is constant
c
Dimensional analysis can enable a process in the laboratory to be scaled up to an industrial process. If the industrial process uses the same fluid but larger diameter pipes than the lab-scale process, then average fluid velocities in the lab-scale process should be_________________the average fluid velocities in the industrial process. a) less than b) equal to c) greater than
c
Dip-coating provides a way to rapidly deposit a protective smooth colored plastic or polymer surface on metal wires and hooks (see figure). After the hooks are dipped in the polymer solution, they are lifted out and excess solution flows from the hooks back into the dipping solution. Assume the hook may be approximated by a cylinder with length L and radius R, the z direction points out from bottom to upper of the coating liquid; as the excess solution flows down the surface of each hook, it exerts a force that could be best approximated by an expression: hooks into a coating a) Fz=∫L0∫2π0(−τrz)|r=Rdθdz b) Fz=∫L0∫2π0τrz|r=Rdθdz c) Fz=∫L0∫2π0(−τrz)|r=RRdθdz d) Fz=∫L0∫2π0τrz|r=RRdθdz
c
During heating of a semi-infinite slab, the temperature distribution will be a function of both time(t) and the depth(y) into the slab. To solve the partial differential equation that describes the temperature distribution, T(y,t), one needs: a) one initial and one boundary condition b) two boundary conditions c) one initial condition and two boundary conditions d) none
c
For turbulent flow in a tube, fluid velocities that are measured at a fixed radial location typically exhibit significant fluctuations over time. To characterize such velocities, a process of time-smoothing is often performed. 1) To calculate a time-smoothed velocity, the instantaneous velocity is integrated over a time period T, and the integrated value is then divided by T. The duration of T must be a) shorter than the duration of a typical velocity fluctuation b) the same order of magnitude of a typical velocity fluctuations c) longer than the duration of a typical velocity fluctuation
c
Heat conduction (3 points). Solid materials A and B are of equal thickness, L, and arranged as shown in the figure. The temperature at x = 0 is 100°C, and the temperature at x = 2L is 20°C. At steady state what is the temperature at x = L if the thermal conductivity of material B is 3-fold larger than the thermal conductivity of material A? Quiz 9 problem 6 image a) 25 C b) 33.3 C c) 40 C d) 75 C e) 80 C
c
In its most general formulation, Newton's Law of Viscosity (Appendix B.1, BSLK) describes for 3-dimensional time-dependent flow how the shear stress depends on velocity gradients; it is a a) scalar equation b) vector equation c) tensor equation
c
Introduction. Consider two immiscible (non-mixing) Newtonian liquids confined to the space between two parallel flat plates as shown; the lower plate is stationary and the upper plate moves in the positive x-direction with constant velocity V0, and the gravitational force, g, acts in the negative y direction as shown. Assume each liquid occupies an equivalent depth, and liquid 1 is less dense than liquid 2. Consider three cases for steady velocity distributions of the liquids 1) If the two liquids have the same viscosity, then we expect the flow velocity of a) steeper slope in region 1 b) steeper slope in region 2 c) equal slopes in region 1 and 2
c
The drag force that a sphere in a fluid experiences depends on: a) the density of the fluid b) the density of the sphere c) the velocity of the sphere relative to the fluid d) all of the above e) none of the above
c
The magnitude of the buoyancy force that acts on a whale depends on both the volume of seawater displaced by the whale as well as the: a) velocity of seawater relative to the whale b) viscosity of seawater c) density of seawater d) average density of the whale e) none
c
The process of heat transfer from a cooling fin to the ambient air is typically expressed in mathematical terms by assuming the heat flux a) is constant b) depends on the thermal conductivity of the air and temperature gradient between the fin surface temperature and the ambient air c) depends on a heat transfer coefficient and the temperature difference between the fin surface temperature and the ambient air d) none
c
The value of experimentally determined diffusivities (or diffusion coefficients) have been found to span over a more 1030-fold range. The broadest range of diffusivities is exhibited by species as they diffuse in: a) gases b) liquids c) solids
c
The velocity distribution for flow through an annulus includes a dependence of ln(R/r), where r is the coordinate representing the distance from the z-axis in cylindrical coordinates and R is the inner radius of the outer tube. This ln(R/r) term is lacking for the velocity distribution for flow through a circular tube because (choose the best answer): a) the shear stress at r = R must be finite b) the shear stress at r = R must be zero c) the shear stress at r = 0 must be finite d) the velocity distribution must satisfy the no-slip condition at r=R
c
There are benefits to studying the transport of momentum, energy and mass in the same course because they a) often occur at the same time in natural and engineered processes b) are often described by analogous mathematical expressions c) both
c
When the flux of heat at a boundary is modeled using a heat transfer coefficient, then it suggests the heat flux can depend on not only the boundary and ambient temperatures, but it also can depend on a) fluid flows in the ambient environment b) density, thermal conductivity, and heat capacity of the ambient fluid c) a and b d) neither a or b
c
When the flux of heat at a boundary is modeled using a heat transfer coefficient, then it suggests the heat flux can depend on not only the boundary and ambient temperatures, but it also can depend on a) fluid flows in the ambient environment. b) density, thermal conductivity, and heat capacity of the ambient fluid c) both a and b d) neither a or b
c
The process of free (or natural) convection arises in fluid systems where flow is driven by the dependence of: a) fluid heat capacity on temperature b) fluid viscosity on temperature c) fluid thermal conductivity on temperature d) fluid viscosity on pressure e) fluid thermal conductivity on pressure f) none
f
A common approach to solve the partial differential equation that describes the temperature distribution, T(y,t), in question (8) entails seeking a similarity solution that depends on which properties of the slab? a) density b) thermal conductivity c) heat capacity at constant pressure d) all
d
A common material that exhibits an anisotropic thermal conductivity is a) water b) plastic c) brick d) wood
d
Consider a Newtonian fluid between two parallel flat plates as shown; the lower plate is stationary and the upper plate moves in the positive x-direction with velocity V0. Two versions are shown of the same setup; they only differ by the origin of the coordinate system, which is aligned with either the lower plate (left) or the upper plate (right). Which statement below best describes these two systems? Quiz 3 problem 1 image a) Since the two versions are physically identical, both versions will have the same mathematical function for the velocity distribution of interest, vx(y). b) Although the coordinate systems are different for these two versions, the equations for the dependence of the relevant shear stress component, τyxτyx , on y will be identical for the two versions. c) both d) neither
d
Consider a material that is a composite, made of several different materials, each of equal thickness. The transfer of heat through this composite will depend on the overall thermal resistance of the composite, which will be dominated by the material that exhibits the: a) highest heat capacity b) lowest heat capacity c) highest thermal conductivity d) lowest thermal conductivity e) none
d
In spherical coordinates, one may imagine a surface defined by θ=π/9,r=[0,R],ϕ=[0,2π] In words, this surface is defined by a constant value for the angle theta, a radial dimension that spans from the origin to R, and an angle phi that spans from 0 to 2ππ . This surface is best described as a) the surface of a sphere of radius R b) a disc with area ππR2 c) the outer surface of a cylinder with radius R and height of (R)cos(π/9) d) none
d
The Reynolds number is a dimensionless number that depends on a) fluid properties b) a characteristic fluid flow velocity c) a characteristic length scale of the flow geometry d) all e) none
d
The flux of energy as heat often depends on a thermal conductivity or a heat transfer coefficient. How do they differ? a) The thermal conductivity characterizes heat flow at system boundaries, while the heat transfer coefficient is a material property b) The thermal conductivity is combined with a temperature difference to define a heat flux, while the heat transfer coefficient is combined with a temperature gradient to define a heat flux c) The thermal conductivity can depend on the Reynolds number while the heat transfer coefficient is typically independent of Reynolds number d) none
d
The thermal conductivity is a material characteristic that quantifies how effectively the material transports energy as molecular motion or heat. 1) In general gases, liquids, and solids vary in the magnitude of their thermal conductivities as follows (choose the best answer): a) Gases > Liquids > Solids b) Liquids > Gases > Solids c) Liquids > Solids > Gases d) Solids > Liquids > Gases e) Solids > Gases > Liquids
d
The torque required to rotated the viscometer cone in Problem (7), above, depends on the magnitude of: Quiz 4 problem 7 image a) the momentum flux, τϕθ , evaluated at the wetted surface of the cone. b) the momentum flux, τrθ , evaluated at the wetted surface of the cone. c) the momentum flux, τθr , evaluated at the wetted surface of the flat plate. d) the momentum flux, τθϕ , evaluated at the wetted surface of the flat plate. e) the momentum flux, τϕθ , evaluated at the wetted surface of the flat plate.
d
Viscosity has the same units or dimensions as a) time b) pressure c) velocity d) none
d
Viscous dissipation during fluid flow, which generates energy as heat, can cause the temperature of the fluid to increase, especially for fluids with: a) Higher viscosities, higher flow velocities, and higher thermal conductivities b) Lower viscosities, higher flow velocities, and higher thermal conductivities c) Higher viscosities, lower flow velocities, and higher thermal conductivities d) Higher viscosities, higher flow velocities, and lower thermal conductivities
d
1) Consider a Newtonian fluid between two parallel flat plates as shown; the lower plate is stationary and the upper plate moves in the positive x-direction with constant velocity V0. A distribution of fluid velocity becomes established such that: Quiz 4 problem 1 image a) both the velocity and shear stress distribution are linear functions of y. b) both the velocity and shear stress distribution are parabolic functions of y. c) the velocity distribution is parabolic with respect to y, and the shear stress distribution is linear with respect to y. d) the velocity distribution is linear with respect to y, and the shear stress distribution is parabolic with respect to y. e) none
e
Laminar annular flow with inner cylinder moving axially. Consider the system shown below, in which a cylindrical rod is being moved with a velocity V through a narrow cylinder. The rod and the cylinder are coaxial and the fluid is Newtonian. To determine the velocity profile of the fluid within the narrow annular region using the Navier-Stokes equations which of the following terms is the most relevant? (choose one) Quiz 6 problem 8 image a) ∂vz/∂z b) ∂vr/∂z c)∂/∂r(1/r∂(rvr)/∂r) d) ∂^2vr/∂z^2 e) 1/r(∂/∂r(r∂vz/∂r))
e
On the first day of your internship, your boss gives you a timer and suggests that it may be useful for your first project. Her plan is for you to characterize of a novel polymer solution. She has planned that for you to measure what property of the polymer solution? (Hint: consider the units or dimensions associated with each possible answer) a) density b) heat capacity c) mass fraction of polymer in the solution d) solvent content e) viscosity
e
The velocity distribution of a falling film depends on what assumptions? a) The fluid flow is not steady (or the flow is accelerating) b) The fluid does not follow Newtonian's Law of Viscosity (it is a non-Newtonian fluid) c) The fluid flow can be turbulent d) The flow at the fluid-solid boundary can slip. e) none
e
To develop an approximate analytical solution for the temperature of the fluid leaving the tube described in question (2), we assume that the: The heating of a fluid of known temperature as it flows through a single heated tube. a) fluid viscosity, heat capacity at constant pressure, and density are constant b) fluid viscosity, heat capacity at constant pressure, and density depend on the fluid temperature c) viscous dissipation and bouyancy effects are significant d) the tube is of sufficient length that the radial and axial components of the temperature profile can be uncoupled e) a and d f) b and c g) none
e
The process of free (or natural) convection arises in fluid systems where flow can arise in the absence of a gravitational force; this statement is: true / false
false
Shear rate has the same units or dimensions as a) time b) pressure c) velocity d) none
none
Shear stress has the same units or dimensions as a) time b) pressure c) velocity d) none
pressure
Approximate analytical solutions for the temperature of the fluid leaving the heated tube described in question (2) will eventually fail when the dependence of fluid properties on temperature can no longer be neglected; this statement is The heating of a fluid of known temperature as it flows through a single heated tube. true / false
true
The Reynolds number is useful because its magnitude can describe differences in flow behaviors, including transitions from laminar to turbulent flow. This statement is true / false
true
The continuum assumption is useful in the study of transport phenomena because it enables us to treat fluid properties (e.g., density, pressure, temperature and bulk velocity) as well-defined at length scales that are small relative to the size of the systems we study, but large relative to the molecular scale. This statement is true or false
true
The equation of continuity is valid for a compressible ideal gas of variable density. This statement is True / False
true
When we study laminar fluid flows in different geometries, we often start by listing assumptions about the fluid and its properties, as well as components of the velocity vector that we anticipate will be either negligible or important. By using the equation of continuity to test such assumptions we sometimes arrive at a result: 0 = 0 (zero equals zero), which is useful because it indicates that our assumptions do not violate the equation of continuity. This statement is true / false
true
Flow of a falling film. The falling-film flow shown in the figure may be used to derive the following expression for the velocity distribution: vz(x)=ρgδ^2cosβ/(2μ)[1−(x/δ)^2] Quiz 3 problem 6 image τxz(x)=
ρgcos(β)x
