Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Textbook Question
Chapter 7, Problem 39P
The rate dT/dt at which the temperature T at the center of a rice kernel falls during a food technology process is critical—too high a value leads to cracking of the kernel, and too low a value makes the process slow and costly. The rate depends on the rice specific heat, c, thermal conductivity, k, and size, L, as well as the cooling air specific heat, cp, density, ρ, viscosity, μ, and speed, V. How many basic dimensions are included in these variables? Determine the Π parameters for this problem.
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1.
Start from the following equations from class notes (treat as given):
The shear stress in pipe flow T = -μ- dr
du
16 [1-(-)²),
AP D²
16μL
The fluid velocity in the pipe u =
Derive clearly the following results:
(a) The shear stress on the wall of the pipe, Tw.
(b) The average velocity in the pipe flow, ū.
(c) The Darcy friction factor, defined by f
where L is the length of the pipe.
8 tw
pū²
(d) Express the result of (c) in terms of the Reynolds number, Re.
(e) Find an expression for the head loss due to shear stress at the wall, AH₁, in terms of
f,u, D and L.
(f) What are the main assumptions in the fluid flow, in order to analyse the flow in this
way?
A mass of 1.25 kg stretches a spring 0.06 m. The mass is in a
medium that exerts a viscous resistance of 66 N when the mass
m
has a velocity of 6 . The viscous resistance is proportional to the
-
S
speed of the object.
Suppose the object is displaced an additional 0.03 m and released.
Find an function to express the object's displacement from the
spring's natural position, in m after t seconds. Let positive
m
as the
s2
displacements indicate a stretched spring, and use 9.8
acceleration due to gravity.
u(t) =
%3D
Three pipes A. B, and C are interconnected as shown in figure 1. The pipe dimensions
are as follows:
Pipeline
A
D (cm)
15
10
L (m)
300
240
600
0.01
0.01
0.005
B
20
A
15 m
25 m
B
Figure 1
1.1 Find the rate at which water will flow in each pipe, ignoring the shock losses at P
and entry to pipelines A and B.
1.2 Find the pressure at P.
Chapter 7 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 7 - The slope of the free surface of a steady wave in...Ch. 7 - One-dimensional unsteady flow in a thin liquid...Ch. 7 - In atmospheric studies the motion of the earths...Ch. 7 - Fluid fills the space between two parallel plates....Ch. 7 - By using order of magnitude analysis, the...Ch. 7 - Consider a disk of radius R rotating in an...Ch. 7 - An unsteady, two-dimensional, compressible,...Ch. 7 - Experiments show that the pressure drop for flow...Ch. 7 - At very low speeds, the drag on an object is...Ch. 7 - We saw in Chapter 3 that the buoyant force, FB, on...
Ch. 7 - Assume that the velocity acquired by a body...Ch. 7 - Derive by dimensional analysis an expression for...Ch. 7 - The speed of shallow water waves in the ocean...Ch. 7 - The speed, V, of a free-surface wave in shallow...Ch. 7 - The boundary-layer thickness, , on a smooth flat...Ch. 7 - The speed, V, of a free-surface gravity wave in...Ch. 7 - Derive an expression for the velocity of very...Ch. 7 - Derive an expression for the axial thrust exerted...Ch. 7 - Derive an expression for drag force on a smooth...Ch. 7 - The energy released during an explosion, E, is a...Ch. 7 - Measurements of the liquid height upstream from an...Ch. 7 - The load-carrying capacity, W, of a journal...Ch. 7 - Derive an expression for the drag force on a...Ch. 7 - A circular disk of diameter d and of negligible...Ch. 7 - Two cylinders are concentric, the outer one fixed...Ch. 7 - The time, t, for oil to drain out of a viscosity...Ch. 7 - You are asked to find a set of dimensionless...Ch. 7 - A continuous belt moving vertically through a bath...Ch. 7 - Derive an expression for the frictional torque...Ch. 7 - Tests on the established flow of six different...Ch. 7 - The power, P, required to drive a fan is believed...Ch. 7 - The sketch shows an air jet discharging...Ch. 7 - The diameter, d, of bubbles produced by a...Ch. 7 - Choked-flow nozzles are often used to meter the...Ch. 7 - A large tank of liquid under pressure is drained...Ch. 7 - Spin plays an important role in the flight...Ch. 7 - The power loss, P, in a journal bearing depends on...Ch. 7 - The thrust of a marine propeller is to be measured...Ch. 7 - The rate dT/dt at which the temperature T at the...Ch. 7 - When a valve is closed suddenly in a pipe with...Ch. 7 - An airship is to operate at 20 m/s in air at...Ch. 7 - An airplane wing of 3 m chord length moves through...Ch. 7 - A flat plate 1.5 m long and 0.3 m wide is towed at...Ch. 7 - This 1:12 pump model using water at 15C simulates...Ch. 7 - An ocean-going vessel is to be powered by a...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - A 1:3 scale model of a torpedo is tested in a wind...Ch. 7 - A flow rate of 0:18 m3/s of water at 20C...Ch. 7 - A force of 9 N is required to tow a 1:50 ship...Ch. 7 - An airplane wing, with chord length of 1.5 m and...Ch. 7 - A water pump with impeller diameter of 24 in. is...Ch. 7 - A model hydrofoil is to be tested at 1:20 scale....Ch. 7 - A ship 120 m long moves through freshwater at 15C...Ch. 7 - A 1:30 scale model of a cavitating overflow...Ch. 7 - In some speed ranges, vortices are shed from the...Ch. 7 - A 1:8 scale model of a tractor-trailer rig is...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - When a sphere of 0.25 mm diameter and specific...Ch. 7 - The flow about a 150 mm artillery projectile which...Ch. 7 - Your favorite professor likes mountain climbing,...Ch. 7 - A 1:50-scale model of a submarine is to be tested...Ch. 7 - Consider water flow around a circular cylinder, of...Ch. 7 - A 1:10 scale model of a tractor-trailer rig is...Ch. 7 - The power, P, required to drive a fan is assumed...Ch. 7 - Over a certain range of air speeds, V, the lift,...Ch. 7 - The pressure rise, p, of a liquid flowing steadily...Ch. 7 - An axial-flow pump is required to deliver 0.75...Ch. 7 - A model propeller 1 m in diameter is tested in a...Ch. 7 - Consider Problem 7.38. Experience shows that for...Ch. 7 - Closed-circuit wind tunnels can produce higher...Ch. 7 - A 1:16 model of a bus is tested in a wind tunnel...Ch. 7 - The propagation speed of small-amplitude surface...
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