ME 3111 Ch 3
The linear momentum equation when a control volume has one-dimensional inlets and outlets is given by Σ F =ddt(∫CVVρdV)Σ F =ddt∫CVVρdV _____, where m is the mass flow rate and V is the fluid velocity relative to an inertial (nonaccelerating) coordinate system.
+ Σ(miVi)out − Σ(miVi)in
When Reynolds transport theorem is applied to the law of conservation of mass, the rate of change of mass with respect to time will be equal to ___ .
0
Identify examples of noninertial reference frame.
Coordinates fixed to a rocket during take off Any flow on earth's surface which is accelerating relative to the fixed stars
In the Bernoulli equation a relation exists between velocity, elevation in a frictionless flow, and _____.
pressure
The _____ pressure is the highest pressure possible in the flow, if elevation changes are neglected
stagnation
In a control volume, the time derivative of volume integral in the Reynolds transport theorem vanishes only if _____.
steady
If the control volume moves with a uniform velocity that retains its shape, then _____.
the control volume elements do not change with time
If density varies over a surface, mass flow rate can be represented as _____.
∫sρVndA
The total pressure work (W˙p)W˙p equation is _____.
∫CSp (V·n)dA
Identify the laws that are suitable for arbitrary regions in a flow across a control volume.
Conservation of mass The energy equation Linear momentum relation
An incompressible fluid flows through a duct having a cross-sectional area of 1 m2 at 2 m/s. The density of the fluid is 1000 kg/m3. Determine the mass flow rate of the fluid.
2000 kg/s
In a frictionless flow the Bernoulli constant ωo = p^2/ρ + V^2/2 + gz remains the same. Identify a true statement of frictionless flow.
A frictionless flow region is irrotational.
Identify examples of noninertial reference frame
Any flow on earth's surface which is accelerating relative to the fixed stars Coordinates fixed to a rocket during take off
The first law of thermodynamics states that the change in the internal energy (E) of a system is the difference between the heat added (Q) and the work (W) produced. The dummy variable for the Reynolds transportation theorem when it is applied to derive the first law of thermodynamics will be _____.
E
Identify the assumptions that were made to derive the Bernoulli equation.
Flow along a single streamline Steady flow Incompressible flow
Which of the following systems can be analyzed by a fixed control volume?
Flow through a nozzle having an exit velocity of 75 m/s
Identify the factors that are included in Bernoulli's energy relation.
Kinetic energy change Pressure work Potential energy change
Identify the true statement of the Bernoulli equation.
The Bernoulli equation does not account for possible energy exchange due to heat or work.
Identify a true statement about the conservation of mass law for a control volume that has one-dimensional inlets and outlets.
The algebraic sum of integral value of time derivative of density and the overall mass flow rate within a control volume equals to zero.
For a control volume, the relative velocity Vr=VVr=V and linear momentum equation is Σ F =ddt(∫CVVρdV)+∫CSVρ(V·n)dAΣ F =ddt∫CVVρdV+∫CSVρ(V·n)dA, where V is the fluid velocity relative to an inertial coordinate system, VrVr is the relative velocity of fluid crossing the control surface, n is the unit vector normal to a small cross-sectional area dA, ρ is the density of the fluid flowing through the small cross section dA, CV represents the control volume, and CS represents the control surface.
The control volume must be fixed.
An incompressible fluid flows through a pipe having a uniform cross sectional area of 0.5 m2. The velocity at the inlet is 4 m/s and the density of the fluid is 998 kg/m3. Determine the flow rate.
The correct formula is m⋅=ρAV. Substituting the values, mass flow rate = 1996 kg/s.
Identify the true statements about the application of Reynolds transport theorem on an arbitrary fixed control volume.
The elemental volumes dV do not vary with time. The time derivative of the volume integral vanishes for a constant density and β.
Identify the true statement about a one-dimensional flow over a control surface.
The flow properties are uniform over the cross section.
True or false: For a steady flow control volume with one-dimensional inlets and outlets, the rate of change of mass flow rate of the fluid is zero.
True
True or false: The Bernoulli's relation assumes that no energy exchange occurs due to viscous dissipation and the shaft work.
True
In the energy equation, the shear work due to viscous forces will be equal to zero for _____.
a solid surface
The equation ddt (Bsyst) = ddt (∫CVβρdV) + ∫CS βρVcosθ dAout − ∫CS βρVcosθ dAinddt (Bsyst) = ddt ∫CVβρdV + ∫CS βρVcosθ dAout - ∫CS βρVcosθ dAin is the Reynolds transport theorem for a(n) _____.
arbitrary fixed control volume
When the volume flow rate is multiplied by density, the resultant will indicate the _____.
mass flow rate
In the Bernoulli's equation p1 + 1212ρV12 = p2 + 1212ρV22 = p0 = constant, identify the term that represents stagnation pressure.
p0
Identify the Bernoulli equation for steady frictionless incompressible flow along a streamline, where V is the volume, p is the pressure, ρ is the density, and z is the height of the fluid.
p2−p1/ρ+1/2((V2)^2−(V1)^2)+g(z2−z1)=0
The mass conservation equation (ρAV) = -v∂ρ∂t∂ρ∂t A ds does not require an assumption of _____, where V is the volume, P is the pressure, is the ρ density, A is the cross sectional area, s is the streamline direction, and v is the velocity of the fluid.
frictionless flow
The area integral of the Reynolds transport theorem will become complicated when the control volume _____.
has constant shape and variable velocity
If the velocity of a flow is doubled, the dynamic pressure of a flow will _____.
increase by a factor of 4
In fluid mechanics, Newton's second law is called the _____.
linear momentum relation
The Bernoulli's equation represents the pressure, potential, and kinetic energies as heads of fluid column. In order to represent them in SI unit of power, the net head must be multiplied with _____.
mass flow rate
The inlet and outlet surfaces are chosen to be normal to the flow, in order that _____.
the normal velocity equals the actual velocity pressure is the dominant force
The average velocity when multiplied by the section area gives the _____.
volume flow rate
Identify a form of Newton's law for a noninertial reference frame.
ΣF - marel = m dvdt
