Q. A horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1\ {ms}^{- 1}$ when pressure is 50 kPa at a point. If the velocity of flow has to be $2\ {ms}^{- 1}$ at some other point, the pressure at that point should be
A) 50 kPa
B) 100 kPa
C) 48.5 kPa
D) 24.25 kPa
Explanation
(c) According to Bernoulli’s equation for horizontal pipe,
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$p_{1} + \frac{1}{2}\rho v_{1}^{2} = p_{2} + \frac{1}{2}\rho v_{2}^{2}$
$\Longrightarrow \ p_{1} + \frac{1}{2}\rho\left( v_{1}^{2} - v_{2}^{2} \right) = p_{2}$
$\Longrightarrow \ \ \ \ \ \ p_{2} = 50 \times 10^{3} + \frac{1}{2} \times 10^{3} \times \left( 1^{2} - 2^{2} \right)$
$\Longrightarrow \ \ \ p_{2} = 50 \times 10^{3} - 1.5 \times 10^{3}$
$= 48.5\ kPa$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.