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Chapter 10: Q17P (page 260)

(II) A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61掳 from the horizontal (Fig. 10鈥�49). (a) Determine the water gauge pressure at the house. (b) How high could the water shoot if it came vertically out of a broken pipe in front of the house?

Short Answer

Expert verified

  1. The water gauge pressure at the house is 0.70 脳 106 Pa.

  2. The height of the water from the broken pipe is 71.6m.

Step by step solution

01

Understanding the fluid pressure

The effective pressure for a fluid relies on its density, depth, and gravitational acceleration.

02

Given the data

The depth of the water tank is h = 6.0m.

The length of the pipe is l =75m.

The angle of the pipe with the horizontal is 胃 = 61掳.

The schematic diagram of the situation is here:

03

Calculation for the effective pressure

The acceleration due to gravity is g =9.8m/s2.

Now the effective vertical height of the water from the free surface to the bottom of the pipe at the house is,

The pressure due to water is calculated as,

Hence, the water gauge pressure at the house is 0.70脳 106 Pa.

04

Calculation the height of the water

Now if the water comes vertically from the broken pipe it will come to a vertical height as follows:

Hence, the height of the water from the broken pipe is 71.6 m.

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