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College Physics (Urone)
Found in: Page 425

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Short Answer

What is the difference between flow rate and fluid velocity? How are they related?

The fluid velocity is variation in position with time while the flow rate is the quantity of water passed per second from an area and the flow rate is equal to the product of cross section area and fluid velocity.

See the step by step solution

Step by Step Solution

Step 1: Difference between flow rate and fluid velocity

The fluid velocity of a fluid is the variation in the position of the fluid with time and position. The volume of moving fluid that passes through a certain area of cross section in unit time is called the flow rate.

Step 2: Relation between fluid velocity and flow rate

Suppose a fluid is moving with fluid velocity \({\rm{v}}\) through a cross-section of the area \({\rm{A}}\) with diameter \({\rm{d}}\).

The cross-section area for fluid flow is given as:

\({\rm{A}} = \frac{{\rm{\pi }}}{{\rm{4}}}{{\rm{d}}^{\rm{2}}}\)

The flow rate of fluid is given as:

\({\rm{Q}} = {\rm{Av}}\)

Here, \({\rm{Q}}\) is the flow rate and \({\rm{v}}\)is the fluid velocity.

Substitute all the values in the above equation.

\(\begin{array}{l}{\rm{Q}} = \left( {\frac{{\rm{\pi }}}{{\rm{4}}}{{\rm{d}}^{\rm{2}}}} \right){\rm{v}}\\{\rm{Q}} = \frac{{\rm{\pi }}}{{\rm{4}}}{{\rm{d}}^{\rm{2}}}{\rm{v}}\end{array}\)

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