   Chapter 5, Problem 56P

Chapter
Section
Textbook Problem

A certain rain cloud at an altitude of 1.75 km contains 3.20 × 107 kg of water vapor. How long would it take for a 2.70-kW pump to raise the same amount of water from Earth’s surface to the cloud’s position?

To determine
The time required to raise the water using pump from ground level to cloud level.

Explanation

Given Info:

The altitude of the rain cloud is 1.75km .

The water vapor contained in the rain cloud is 3.20×107kg .

The power of the pump is 2.70kW .

If the variation of gravity is considered as negligible,

Formula to calculate the time required to the work is,

Δt=WP

• W is the work which is required to lift the cloud at constant speed to the altitude.
• P is the power of pump

Thus,

Δt=mg(Δh)P

• Δh is the altitude to which the cloud to be lifted
• m is mass of the water vapor in cloud
• g is acceleration due to gravity

Substitute 3.20×107kg for m, 9.8m/s2 for g, 1.75km for Δh and 2

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