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 8, Problem 49P
In a food industry plant, two immiscible fluids are pumped through a tube such that fluid 1(μ1 = 0.5 N·s/m2) forms an inner core r = D/4 and fluid 2(μ2 = 5 N·s/m2) forms an outer annulus. The tube has D = 5 mm diameter and length L = 5 m. Derive and plot the velocity distribution if the applied pressure difference, Δp, is 5 MPa.
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R₂ = 20 mm
Flow-
Liquid
p= 1000 kg/m³
μ = 0.02 Pa s
Ri. A
Ro
A liquid flows through the space between a small rod and a pipe, as shown in diagram below.
The outer radius of the pipe is R₁, the inner radius of the rod is R₁, and the ratio λ
pressure difference per unit length (Ap/L) of 2000 Pa/m is applied to drive the fluid flow. The
liquid has a viscosity of μ = 0.02 Pa's.
Q = π
If the equation of volumetric flow rate (Q) of the liquid, is given as
ApR" ApR" (Ri
8μ L 8μ L
+
-20%
4
R
R₁ = AR₁ = 10 mm
+
Ro
Ri
(A) What should be the value of "n", for the equation above to be dimensionally consistent? Use
dimensional analysis.
n
(1-2²)² ApR"
8μ L
In
==.
(B) Calculate the value of volumetric flow rate in cubic meter per second when r = (Ro+
R₁)/2, and Ro = 20mm, R₁ = 10mm. Report your result with three significant figures.
Problem
Consider a cylindrical pipe of length L and diameter D = 2R. The angle that the axis of the pipe forms with
the vertical direction is a. Assume that when the fluid enters the pipe its velocity is uniform (i.e., it has the
same value over the entire cross-section of the pipe) and equal to U in the axial direction. In the radial and
angular directions, the velocity is zero. So, it is:
2 =0: v(r, 0, 2) = Ue,
(1.1)
Here v is the fluid velocity and e, is a vector of unit magnitude parallel to the coordinate axis z; furthermore,
we have assumed that the pipe inlet is located at z = 0.
Near the entrance of the pipe, the velocity profile varies in the axial direction. But after a certain entrance
length, the profile becomes fully developed, no longer changing with z. The evolution of the velocity profile
is sketched in Fig. 1, where, for clarity, the pipe inclination is not shown. The entrance length is denoted by
L.. For z > L., the fluid velocity is no longer a function of the axial…
Given an open tank filled with oil that is discharging through a 35-meter long
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h = 5 m
Ro = 5 cm
%D
Ri = 2 cm
Q. V
L= 35 m
Oil (SG = 0.9)
%3D
Chapter 8 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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