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Chapter 14: Q55P (page 410)

How much work is done by pressure in forcing 1.4m3of water through a pipe having an internal diameter of 13mmif the difference in pressure at the two ends of the pipe is 1.0atm?

Short Answer

Expert verified

Work done by pressure to force the water through a pipe is 1.4×105J.

Step by step solution

01

Given information

  • The volume of water flowing through the pipe isV=1.4m3

  • The pressure difference between two ends of the pipe is

∆ρ=1.0atm

=1.01×105Pa

02

Determining the concept of work done

The work done is the product of force and displacement. It can also be written in terms of change in pressure and volume.

Using the formula for work done, find the work done by pressure to force the water through the pipe.

The formula is as follows:

W=pv

where, Wis work done, pis pressure andVis volume.

03

Determining the work done by pressure to force the water through the pipe

The equation for work done can be written as,

W=p×v

Here, the volume of water remains constant, and only pressure changes. So,

Wp=v

Substituting the given values,

W=(1.01×105Pa)×1.4m3

=1.4×105J

Hence, work done by pressure to force the water through pipe is 1.4×105J.

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