When a garden hose with an output diameter of 20 is directed straight upward, the stream of water rises to a height of 0.19 mm . You then use your thumb to partially cover the output opening so that its diameter is reduced to 10 . Part A How high does the water rise now? Ignore drag and assume that the smaller opening you create with your thumb is circular.

3.04 m

Explanation:

20 mm = 0.02 m

10 mm = 0.01 m

When the water escape from the hose opening with a velocity v to rise up to a height of 0.19m, its potential energy is converted from kinetic energy:

where m is the mass and h is the vertical distance traveled, and g = 9.81m/s2 is the gravitational acceleration

We can divide both sides by m and get:

(1)

When you cover part of the hose and reduce the cross sectional area, water velocity increases:

As the area of the circular opening is:

where d is the diameter

From equation (1) we have the following ratio

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