Fluids: Chapters 7 & 8

What are the two types of energy losses?

-Friction loss due to wall shear stress (tao w) -Minor loss due to local geometric changes

At large Reynolds numbers

-the inertial forces are large relative to the viscous forces -the viscous forces cannot prevent the random and rapid fluctuations of the fluid (turbulent)

The rule of thumb is that the Mach number must stay below about __ in order for the flow field to be considered "incompressible".

0.3

Open-channel flow

A pipe that is partially filled with a flowing fluid

What is the purpose of pressurizing a wind tunnel?

A pressurized wind tunnel can achieve higher Reynolds number for the same scale model

To achieve exact similitude, the model must __ and values of Pi groups must __

Be a scale model of the prototype (geometric similitude); be the same for the model and the prototype (dynamic similitude) (In practice its not always possible to have complete similitude, so only the significant Pi groups are needed to be matched)

The Reynolds number at which the flow becomes turbulent is called

Critical Reynolds number

A way to measure a physical quantity (without numerical values)

Dimension

The law of dimensional homogeneity states

Every additive term in an equation must have the same dimensions (ex: energy equation for incompressible flow)

(T/F) The primary reason for nondimensionalizing an equation is to increase the number of parameters in the problem.

False;

Hydrodynamically developing flow

Flow in the entrance region (where velocity profile develops)

Consider the flow of air and water in pipes of the same diameter, same temperature, and at the same mean velocity. Which flow is more likely to be turbulent?

Flow of water

__ similarity is a condition in which the model must be the same shape as the prototype, but scaled by some constant scale factor.

Geometric

Most important forces in open hydraulic structures and minimum requirements

Gravitational force- due to changes in water surface elevation Viscous forces- often small relative to gravitational forces (spillways, channel transitions, weirs) Minimum requirements: Froude number similitude

Buckingham Pi Theorem states

If a system has n variables with k basic dimensions, then the system can be expressed by n-k independent dimensionless variables

When is Reynolds number important?

In all types of fluid mechanics problems

When is Froude number important?

In flow with a free surface

When is Mach number important?

In supersonic flow

If the air pressure in the tunnel increases by a factor of 1.8, all else being equal (same wind speed, same model, etc.), by what factor will the Reynolds number increase?

Increase by a factor of 1.8

Consider fully developed laminar flow in a circular pipe. If the diameter of the pipe is reduced by half while the flow rate and the pipe length are held constant, the head loss will __.

Increase by a factor of 16

Pi groups are also known as

Independent dimensionless variables

A piping system involves sharp turns, and thus large minor head losses. One way of reducing the head loss is to replace the sharp turns by circular elbows. What is another way?

Install turning vanes inside the elbows

Which factor has a greater minor loss coefficient during pipe flow?

Instantaneous expansion

What is the expression for minor loss coefficient KL?

KL= hL/(V^2/2g)

Identify the primary dimensions of kinematic viscosity.

L^2T^-1

What are the basic/primary dimensions?

Length (L), time (T), mass (M), and sometimes temperature (theta)

The head losses associated with the flow of a fluid through fittings, valves, bends, elbows, tees, inlets, exits, enlargements, contractions, etc. are called __ losses.

Minor

Relaxed similitude requirements

Need to determine which forces are the most important in the flow and attempt to keep those force ratios the same

The effect of rounding a pipe exit on the loss coefficient is __.

Negligible

The primary dimensions of the dependent variables or pi groups in a general flow are

P {M/LT^2}, Tau or delta P {M/LT^2}, F {ML/T^2} (3 dependent; 4 independent)

It is impossible to have all force ratios the same unless the model is the __ as the prototype

Same size

Geometric similarity

Shape should be the same (the model must be the same shape as the prototype, but may be scaled by some constant scale factor)

Transition

The flow fluctuates between laminar and turbulent flows; Re less than or equal to 4000 and greater than or equal to 2300

The basic requirement for dynamic similitude is

The forces that act on corresponding masses in the model and prototype must be in the same ratio (constant) throughout the entire flow field (Fm/Fp= constant); they will have the same flow patterns

Irrotational (core) flow region

The frictional effects are negligible and the velocity remains essentially constant in the radial direction

Hydrodynamic entry length (Lh)

The length of hydrodynamic entrance region

Dynamic similarity

The non dimensional numbers that characterize forces should be equal (Buckingham pi theorem)

Hydrodynamically fully developed region

The region beyond the entrance region in which the velocity profile is fully developed and remains unchanged

Hydrodynamic entrance region

The region from the pipe inlet to the point at which the boundary layer merges at the centerline

(T/F) The law of dimensional homogeneity states that every additive term in an equation must have the same dimensions.

True

A way to assign a number to a dimension

Unit

During a retrofitting project of a fluid flow system to reduce the pumping power, it is proposed to install vanes into the miter elbows or replace the sharp turns in 90 degree miter elbow by smooth curved bends. Which approach will result in a greater reduction in pumping power requirements?

Using miter elbow with vanes

Kinematic similarity

Velocity and acceleration should be proportional

The effect of rounding a pipe inlet on the loss coefficient is __.

Very significant

Most important force in glows without free surface effects and minimum requirements

Viscous force- Reynolds number in the model must equal the Reynolds number in the prototype (closed conduits, pipe flow, wind tunnel) Minimum requirements: Reynolds number similitude

Consider a person walking first in air and then in water at the same speed. For which motion will the Reynolds number be higher?

Walking in water

Fully developed

When both the velocity profile and the normalized temperature profile remain unchanged

Internal flow

a conduit (any pipe, tube, or duct) that is completely filled with a flowing fluid and driven by a pump or fan, where we pay particular attention to the friction

The pressure drop is __ in the entrance regions of a pipe, and the effect of the entrance region is always to __ the average friction factor for the entire pipe

higher; increase

All dimensionless groups can be explained by the ratio of __ to some force.

inertia (kinetic)

Laminar flow

smooth streamlines and highly ordered motion; Re less than or equal to 2300

Velocity boundary layer

the region of the flow in which the effects of the viscous shearing forces caused by fluid viscosity are felt

Boundary layer region

the viscous effects and the velocity changes are significant

At small or moderate Reynolds numbers

the viscous forces are large enough to suppress these fluctuations and to keep the fluid in line (laminar)

Turbulent flow

velocity fluctuations and highly disordered motion; Re greater than or equal to 4000

The moment of force (M) is formed by the cross product of a moment arm (r) and an applied force (F) M= r x F. Identify the primary dimensions of (M).

{M} = {ML^2T^-2}

Identify the primary dimensions of acceleration.

{a} = {LT^-2}

Identify the primary dimensions of angular acceleration.

{a} = {T^-2}

Identify the primary dimensions of angular velocity.

{w} = {T^-1}