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Q.29

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 384

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Short Answer

A bucket is filled with water to a height of , then a plug is removed from a hole in the bottom of the bucket. As the water begins to pour out of the hole, how fast is it moving

The speed of water flowing out of the hole is .

See the step by step solution

Step by Step Solution

Step 1: Expression for Bernoulli's equation 

The expression for Bernoulli's equation for a flowing fluid, between two points and is written as,

Here, is the pressure at point , is the pressure at point , is the velocity at point , is the velocity at point , is the position of point above the datum, is the position of point above the datum and is the density of the flowing fluid.

Step 2: Continuity equation 

Continuity equation between the above mentioned points is written as,

Here, and are the cross-sectional areas of the flow at the points and , respectively.

Step 3: Calculation of speed of water flow

Understand that point is the top of the bucket and the point is at the hole. The height is measured from the top of the bucket. The pressure at points and is atmospheric pressure. So,

Here, is atmospheric pressure.

Also,

It is known that area of hole is much smaller to the area of water at the top of the bucket. Hence,

Apply continuity equation between points and

Use equations and , to get:

Squaring both sides of the equation.

Hence can be neglected.

Substitute for and, for and for .

Substitute for and for ,

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