Question

The rate of flow of the liquid is the product of:
A) Area of cross section of the liquid and velocity of the liquid
B) Length of the tube of the flow and velocity of the liquid
C) Volume of the tube of the flow and velocity of the liquid
D) Viscous force acting on the liquid layer and velocity of the liquid.

Answer 1

To answer this question, the rate of flow of liquid should be defined and hence, its unit. Then, the units of the options should be multiplied to match with the unit of rate of flow of liquid, to obtain the answer.

Complete step by step answer:
The rate of flow of liquid is a quantity that represents how much fluid passes through the given area in consideration, per unit time. For an incompressible fluid, we consider the volume flow rate, where the rate of flow is defined as the volume of fluid that passes per unit time.
Hence, by the definition, the unit of rate of flow is –
$Q = \dfrac{V}{t} = \dfrac{{{m^3}}}{\operatorname{s} }$
Let us consider the units obtained by the product of the units of the quantities in each option.
Option A: Area and Velocity.
Area is measured in ${m^2}$
Velocity is measure in $\dfrac{m}{s}$
Multiplying, we get –
${m^2} \times \dfrac{m}{s} = \dfrac{{{m^3}}}{\operatorname{s} }$
This matches with the calculated unit.
Hence, this option is correct.

Option B: Length and Velocity.
Length is measured in $m$
Velocity is measure in $\dfrac{m}{s}$
Multiplying, we get –
$m \times \dfrac{m}{s} = \dfrac{{{m^2}}}{\operatorname{s} }$
This does not match with the calculated unit.
Hence, this option is incorrect.

Option C: Volume and Velocity.
Volume is measured in ${m^3}$
Velocity is measure in $\dfrac{m}{s}$
Multiplying, we get –
${m^3} \times \dfrac{m}{s} = \dfrac{{{m^4}}}{\operatorname{s} }$
This does not match with the calculated unit.
Hence, this option is incorrect.

Option D: Force and Velocity.
Force is measured in $N$
Velocity is measure in $\dfrac{m}{s}$
Multiplying, we get –
$N \times \dfrac{m}{s} = \dfrac{{Nm}}{\operatorname{s} }$
This does not match with the calculated unit.
Hence, this option is incorrect.
Hence, among these options, only the option containing product of area and velocity matches with the rate of flow of fluid.

Hence, the correct option is Option A.

Note: For incompressible fluids, the volume of the fluid is considered. However, for compressible fluids, we have to include the mass flow rate since the density of the fluid changes in the due course of flow and does not remain constant.