
Interpretation: The expression for Hagen-Poiseuille equation in terms of flow rate and pipe diameter is to be determined and consequently change in flow rate.
Concept introduction:
The Hagen-Poiseuille equation is used to determine the pressure drop in the Laminar flow region. The equation for the same is given as,
The notations used here are,
L = Length of the pipe
D = Pipe diameter
The average velocity can also be written as,
Q = Flow rate of the fluid
A = Area of the pipe

Answer to Problem 8.1P
The Hagen-Poiseuille equation in terms of flow rate and diameter is
Explanation of Solution
The area of the pipe is given as,
Substitute equation (3) in equation (2).
Substitute equation (4) in equation (1).
Let subscript 1 for initial conditions and subscript 2 for final conditions.
Keeping all other things constant, the equation (5) can be written as,
This dependency for the two conditions mentioned can be written as.
As diameter is doubled, so D2 = 2D1. From equation (6).
The percentage change in flow rate =
Substitute Q2 = 16Q1,
The percentage change in flow rate =
The Hagen-Poiseuille equation in terms of flow rate and diameter is
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Chapter 8 Solutions
Fundamentals of Momentum, Heat, and Mass Transfer
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