Question

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

Answer 1

Answer: (C)

According to Bernoulli’s equation for horizontal pipe,


$P_{1}+\frac{1}{2} \rho v_{1}^{2}=P_{2}+\frac{1}{2} \rho v_{2}^{2}$
$\Rightarrow P_{1}+\frac{1}{2} \rho\left(v_{1}^{2}-v_{2}^{2}\right)=P_{2}$
$\Rightarrow P_{2}= 50 \times 10^{3}+\frac{1}{2} \times 10^{3} \times\left(1^{2}-2^{2}\right)$
$\Rightarrow P_{2}=50 \times 10^{3}-1.5 \times 10^{3}$
$= 48.5\, kPa$