Answered: Find the head lost due to friction in a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Find the head lost due to friction in a pipe of radius 20 cm and length 50m, through which oil is flowing at a velocity of 5 m/s using (a) Darcy formula (b) Chezy formula for which C= 65, Take Specific gravity of the oil is 0.8 and Dynamic viscosity is 8 X 10-3 poise.

Expert Solution

Step 1 Introduction

In a Flow-through Pipes, losses are classified as

1) Major losses

2) Minor losses

The losses are caused due to

1) Pipe Friction

2) Sudden expansion

3) Sudden Contraction

4) Sudden Bent

Whereas Major Losses comprises of Loss due to friction and it is determined by darcy Weisbach equation and chezy's formula

Step 2 Solution

$\begin{array}{rcl} R_{e} & = & \frac{ρ v D}{μ} \\ = & \frac{800 \times 5 \times 0.4}{0.0008} \\ = & 2000000 \\ f & = & \frac{64}{R_{e}} \\ = & \frac{64}{2000000} \\ = & 3.2 \times 10^{- 5} \\ D a r c y F o r m u l a \\ h_{f} & = & \frac{4 f l v^{2}}{2 g D} \\ = & \frac{4 \times 3.2 \times 10^{- 5} \times 50 \times 5^{2}}{2 \times 9.81 \times 0.4} \\ = & 0.020 m \\ m & = & \frac{D}{4} \\ = & \frac{0.4}{4} \\ = & 0.1 \\ C h e z y' s E q u a t i o n \\ V & = & C \sqrt{m i} \\ V & = & C \sqrt{m \times \frac{h_{f}}{L}} \\ s q u a r i n g o n b o t h s i d e s \\ V^{2} & = & C^{2} \times \frac{D}{4} \times \frac{h_{f}}{L} \\ 5^{2} & = & 65^{2} \times \frac{0.4}{4} \times \frac{h_{f}}{50} \\ h_{f} & = & 2.95 m \end{array}$

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