Question

24.54 The pressure gradient for laminar flow through a constant radius tube is given by where p-pressure (Nm, x (m's), and r= radius (m). distance along the tube's centerline (m), μ dynamic viscosity (N·sm2), Q-flow a. Determine the pressure drop for a 10-cm length tube for a viscous liquid (u 0.005 N s/m2, density - 1x 103 kgm)with a flow of 10x 10-5 m3/s and the following varying radii along its length, x, cm 2 r, mm 2 1.35 1.34 1.6 1.58 1.42 2 b. Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius. C. Determine the average Reynolds number for the tube to verify that flow is truly laminar (Re ,uDu <

Answer 1

clear
clc
close all

mu = 0.005; rhow = 1e3; Q = 10e-6;

x = [0 2 4 5 6 7 10];
r = [2 1.35 1.34 1.6 1.58 1.42 2];

x = x./100; % cm to m
r = r./1000; % mm to m

%%
dp = @(r,dx) (-8*mu*Q./(pi.*r.^4)).*dx;
dx = x-x(1);

%%
pressureDrop = dp(r,dx)

%%
r_avg = mean(r);
pressureDropConstRadius = dp(r_avg,dx)

%%
%compare the pressure drops graphically
plot(x,pressureDrop)
hold on
plot(x,pressureDropConstRadius,'r')
xlabel('x (m)')
ylabel('Pressure drop (N/m^2)')
legend('varying r','constant r')
title('pressure drop for varying r vs for constant r vs length x')

%%
D = 2*mean(r); %average diameter
v = 1.273*Q/D^2; %fluid velocity
Re = rhow*v*D/mu %Reynolds number

1.0e+03 * 0 0.76671.5796-0.9714 1.2258 -2.1921 0.7958 pressureDropConstRadius 1.0e+03 * 0 0.3763 -0.7526 0.9408 1.1290 -1.31711.8816 789.2826

pressure drop for varying r vs for constant r vs length x varying r constant r -500 Z-1000 山 U2 -1500 -2000 2500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 x (m)

COMMENT DOWN FOR ANY QUERY RELATED TO THIS ANSWER,

IF YOU'RE SATISFIED, GIVE A THUMBS UP