Question

A horizontal right angle pipe bend has cross section area $10cm^2$ and water flows through it at speed $ = 20m/s$ . The force on the pipe bend due to the truing of water is
a. $565.7N$
b. $400N$
c. $20N$
d. None of these

Answer 1

Hint: The mass of the water flowing through the pipe at a time will depend on the density of water, cross section area of the pipe and the velocity of water. The force can be defined as the mass multiplied by the change in velocity. Applying those two equations the force on the pipe due to truing of water can be found.

Complete step by step answer:
Given the cross section area of the pipe is $A = 10cm^2 = 1 \times 10^{- 3}m^2$
And the speed of the water is $v = 20m/s$
The expression for the mass flowing per second through the pipe is given as,
$m = \rho \times A \times v$
Where, $\rho $ is the density of the water, $A$ is the cross section area and $v$ is the velocity of the water.
The density of water is $10^3kg/m^3$ .
Substituting the values in the above expression,
$m = 10^3kg/m^3 \times 10^{-3}m^3 \times 20m/s $
$\Rightarrow m = 20kg$
The change in velocity in unit time is given as,
$\dfrac{dv}{dt} = \sqrt{2} \times v$
$\Rightarrow \dfrac{dv}{dt} = \sqrt{2} \times 20m/s $

The water flow inside the pipe due to change in velocity of water will cause the pipe to bend.
According to Newton’s second law of motion, the force is the product of change in velocity and mass of the body.
Therefore, $F = mass \times { \text{change in velocity}}$

Substitute the values in the above expression,
$F = 20kg \times \sqrt{2} \times 20m/s $
$\Rightarrow F = 565.68kgm/s $
$\Rightarrow F= 565.7N$
The force on the pipe bend due to the truing of water is $565.7N$.

Hence, the correct answer is option (A).

Note: We have to note that the velocity of water has a major role in the bending of pipes. If the velocity is greater, greater the force needed to bend the pipe. And if we decrease the area of the cross section the bending of the pipe can be reduced.