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Chapter 1: Q39E (page 390)

Water is flowing in a pipe with a circular cross section but with varying cross-sectional area, and at all points the water completely fills the pipe. (a) At one point in the pipe the radius is 0.150 m. What is the speed of the water at this point if water is flowing into this pipe at a steady rate of 1.20 m3/s? (b) At a second point in the pipe the water speed is 3.80 m/s. What is the radius of the pipe at this point?

Short Answer

Expert verified

Speed of water = 17 m/s

Radius of pipe = 0.32 m

Step by step solution

01

Identification of given data

  • Radius of circle = 0.150 m
  • Flow rate of flow tube = 1.20m3/s
02

Significance of continuity equation

The continuity equation states that no matter where you are along the length of a pipe, the cross-sectional area and fluid velocity will always be the same, regardless of where you are.

03

Calculating speed of water

A1V1=A2V21.20m3s=A2V21.20m3s=π×r2V2

Putting value in equation we get,

V2=1.20m3/sπ×0.150m2=17m/s

04

Calculating flow rate of flow tube

A1V1=A2V21.20m3s=A23.80ms1.20m3/s3.80m/s=A2=π×r2r=0.32m

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