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sludge per unit volume of filtrate, and Rf the specific
resistance of the filter medium. What are the dimensions
of Rf and and a?
7.1.3 WP Verify that the left-hand side of Eq. 7.2 is
dimensionless using the MLT system.
7.1.4 WP The Reynolds number, pVD/u, is a very
important parameter in fluid mechanics. Verify that the
Reynolds number is dimensionless, using both the FLT
system and the MLT system for basic dimensions, and
determine its value for ethyl alcohol flowing at a velocity
of 3 m/s through a 2-in.-diameter pipe.
7.1.5 WP For the flow of a thin film of a liquid with a
depth h and a free surface, two important dimensionless
parameters are the Froude number, V/√gh, and the Weber
number, pv²h/o. Determine the value of these two
parameters for glycerin (at 20 °C) flowing with a velocity
of 0.7 m/s at a depth of 3 mm.
7.1.6 WP The Mach number for a body moving through a
fluid with velocity V is defined as V/c, where c is the speed
of sound in the fluid. This dimensionless parameter is
usually considered to be important in fluid dynamics
problems when its value exceeds 0.3. What would be the
velocity of a body at a Mach number of 0.3 if the fluid is
(a) air at standard atmospheric pressure and 20 °C, and
(b) water at the same temperature and pressure?
Answer
Section 7.3 Determination of Pi Terms
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resistance of the filter medium. What are the dimensions
of Rf and and a?
7.1.3 WP Verify that the left-hand side of Eq. 7.2 is
dimensionless using the MLT system.
7.1.4 WP The Reynolds number, pVD/μ, is a very
important parameter in fluid mechanics. Verify that the
Reynolds number is dimensionless, using both the FLT
system and the MLT system for basic dimensions, and
determine its value for ethyl alcohol flowing at a velocity
of 3 m/s through a 2-in.-diameter pipe.
7.1.5 WP For the flow of a thin film of a liquid with a
depth h and a free surface, two important dimensionless
parameters are the Froude number, V/√gh, and the Weber
number, pV2h/o. Determine the value of these two
parameters for glycerin (at 20 °C) flowing with a velocity
of 0.7 m/s at a depth of 3 mm.
7.1.6 WP The Mach number for a body moving through a
fluid with velocity V is defined as V/c, where c is the speed
of sound in the fluid. This dimensionless parameter is
usually considered to be important in fluid dynamics
problems when its value exceeds 0.3. What would be the
velocity of a body at a Mach number of 0.3 if the fluid is
(a) air at standard atmospheric pressure and 20 °C, and
(b) water at the same temperature and pressure?
> Answer
Section 7.3 Determination of Pi Terms
7.3.1 WP A mixing basin in a sewage filtration plant is
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7.1.5 WP For the flow of a thin film of a liquid with a
depth h and a free surface, two important dimensionless
parameters are the Froude number, V/√gh, and the Weber
number, pv²h/o. Determine the value of these two
parameters for glycerin (at 20 °C) flowing with a velocity
of 0.7 m/s at a depth of 3 mm.
7.1.6 WP The Mach number for a body moving through a
fluid with velocity V is defined as V/c, where c is the speed
of sound in the fluid. This dimensionless parameter is
usually considered to be important in fluid dynamics
problems when its value exceeds 0.3. What would be the
velocity of a body at a Mach number of 0.3 if the fluid is
(a) air at standard atmospheric pressure and 20 °C, and
(b) water at the same temperature and pressure?
Answer
Section 7.3 Determination of Pi Terms
7.3.1 WP A mixing basin in a sewage filtration plant is
stirred by a mechanical agitator with a power input W = F
.L/T. Other parameters describing the performance of the
mixing process are the fluid absolute viscosity μ= F.T/L²,
the basin volume V L³, and the velocity gradient G =
3
1/T. Determine the form of the dimensionless
relationship.
7.3.2 WP SS The excess pressure inside a bubble
(discussed in Chapter 1) is known to be dependent on
bubble radius and surface tension. After finding the pi
terms, determine the variation in excess pressure if we (a)
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7.3.13
Consider a typical situation involving the flow
of a fluid that you encounter almost every day. List what
you think are the important physical variables involved in
this flow and determine an appropriate set of pi terms for
this situation.
7.3.14 WP The weir shown in Fig. P7.3.14 is used to
measure the volume flowrate Q. The height H is a measure
of this flowrate. The weir has length L (perpendicular to
the paper). Select and include relevant fluid properties
and find the appropriate dimensionless parameters.
H
g
Density = p
Absolute viscosity = μ
P
FIGURE P7.3.14
Answer
7.3.15 WP Experiments are conducted on a washing
machine agitator. The relevant dimensional parameters
are the driving torque, J, the oscillation frequency, f, the
angular velocity, w, the number of paddles, N, the paddle
height, H, and the paddle width, w. Specify the relevant
fluid properties and find the appropriate dimensionless
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double the radius and (b) double the surface tension.
Solution
7.3.3 WP At a sudden contraction in a pipe the diameter
changes from D₁ to D2. The pressure drop, Ap, which
develops across the contraction is a function of D₁ and D2,
as well as the velocity, V, in the larger pipe, and the fluid
density, p, and viscosity, μ. Use D₁, V, and μ as repeating
variables to determine a suitable set of dimensionless
parameters. Why would it be incorrect to include the
velocity in the smaller pipe as an additional variable?
7.3.4 WP Water sloshes back and forth in a tank as
shown in Fig. P7.3.4. The frequency of sloshing, w, is
assumed to be a function of the acceleration of gravity, g,
the average depth of the water, h, and the length of the
tank, e. Develop a suitable set of dimensionless
parameters for this problem using g and e as repeating
variables.
@
e
FIGURE P7.3.4
> Answer
7.3.5 WP Assume that the flowrate, Q, of a gas from a
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Spring 2024
Complete the following problems from your textbook. Bolded
problems are candidates for grading, but all must be completed
for full credit.
7.1.4, 7.1.5, 7.1.6, 7.3.14, 7.3.3, 7.9.11