Chapter 12, Problem 1CQ

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

To determine

The difference between flow rate and fluid velocity along with its relation

Answer to Problem 1CQ

Flow rate is given by

  $Q=\frac{V}{t}$

Fluid velocity is given by

  $\stackrel{-}{v}=\frac{d}{t}$

Explanation of Solution

Introduction: Flow rate

can also be defined as volume flow rate, it is a scalar quantity.

Fluid velocity

is a vector quantity.

Flow rate

Q is defined as volume of fluid V passes through cross section A per unit time t.

Mathematically it is given by equation,

  $Q=\frac{V}{t}$

SI unit -

$\frac{m^3}{s}$

CGS unit -

$\frac{c{m}^3}{s}$

Fluid velocity

$\stackrel{-}{v}$is defined as distance travelled by fluid d in certain interval of time t.

Mathematically it is given by equation,

  $\stackrel{-}{v}=\frac{d}{t}$

SI unit -

$\frac{m}{s}$

CGS unit -

$\frac{cm}{s}$

Relation between Flow rate & Fluid velocity Flow rate can be given as

  $\because Q=\frac{V}{t}$

  $=\frac{Ad}{t}$$=A\stackrel{-}{v}$

  $\therefore$ Flow rate = Area of cross section x Fluid velocity.

Conclusion:

The greater the velocity of flow, greater the flow rate.

Flow rate is given by

  $Q=\frac{V}{t}$

Fluid velocity is given by

  $\stackrel{-}{v}=\frac{d}{t}$