Question

In the streamlined flow of a liquid, the power due to the pressure difference between the ends of the tube is
A. Equal to a product of pressure and volume of liquid flowing per second
B. Equal to a product of pressure and mass of liquid flowing per second
C. Equal to the product of radius and coefficient of viscosity
D. Equal to the product of pressure and velocity

Answer 1

Here, we are asked to find the power due to the pressure difference between the ends of the tube in the streamlined flow. For this, first we need to find the work done in the process. After that as per the definition of power which is work done per unit time, we will determine the required power.

Formulas used:
$W = PV$
where, $W$ is the work done, $P$ is the pressure and $V$ is the volume.
$Power = \dfrac{W}{t}$,
where $W$ is the work done and $t$ is the time.

Complete step by step answer:
We know that in the streamlined flow of the liquid, the work done by the liquid is given by the product of pressure and volume of the liquid which means that work done $W = PV$
Now, power in the streamlined flow of liquid can be defined as the work done per second by the liquid. Therefore, we can say that,
$Power = \dfrac{W}{t}$
Now, we will put $W = PV$, therefore the equation of power becomes
$Power = \dfrac{{PV}}{t}$
From this equation, we can say that in the streamlined flow of a liquid, the power due to the pressure difference between the ends of the tube is equal to a product of pressure and volume of liquid flowing per second.

Hence, option A is the right answer.

Note: Here, we have seen the work done by the liquid which may be considered as energy. However, in the streamlined flow of liquid, the loss of energy is minimum because different layers glide over one another without intermixing. Therefore, there is no collision between the molecules of different layers, and hence minimum energy loss.