Question

The equation of continuity is:
A) \[a{{V}^{-1}}=\text{constant}\]
B) \[{{a}^{2}}V=\text{constant}\]
C) \[\dfrac{V}{a}=\text{constant}\]
D) \[aV=\text{constant}\]

Answer 1

Hint: The continuity equation is important for describing the movement of fluids as they pass from a tube of greater diameter to one of smaller diameter. It is important to keep in mind that the fluid should have a constant density as well as it should be incompressible. One of the simplest applications of the continuity equation is determining the change in the fluid velocity due to an expansion or contraction in the diameter of a pipe.

Complete step by step solution:
To understand the continuity equation it helps to consider the flow rate first. The flow rate describes the volume of fluid that passes a particular point per unit time (like how many litres of water per minute are coming out of a pipe).If \[\text{A}\] is the cross-sectional area of the pipe at any point, \[\text{v}\] is the average speed of the flow at that point, the flow rate \[\text{f}\] is given as \[\text{f=Av}\] .

The continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system, hence the flow rate can be said to be constant, that is \[\text{Av}=\text{constant}\].
The same concept is applicable even though more than one flow path may enter or leave the system at the same time.

Therefore, the correct option is (D).

Note: The continuity equation is important for describing the movement of fluids as they pass from a tube of greater diameter to one of smaller diameter. It is important to keep in mind that the fluid should have a constant density as well as it should be incompressible. One of the simplest applications of the continuity equation is determining the change in the fluid velocity due to an expansion or contraction in the diameter of a pipe.