A horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1…

A horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1 \mathrm{~ms}^{-1}$ when pressure is $50 \mathrm{kPa}$ at a point. If the velocity of flow has to be $2 \mathrm{~ms}^{-1}$ at some other point, the pressure at that point should be
  1. $50 \mathrm{kPa}$
  2. $100 \mathrm{kPa}$
  3. $48.5 \mathrm{kPa}$
  4. $24.25 \mathrm{kPa}$

Solution

According to Bernoulli's equation for horizontal pipe,
$\begin{aligned} & P_1+\frac{1}{2} \rho v_1^2=P_2+\frac{1}{2} \rho v_2^2 \\ & \Rightarrow \quad P_1+\frac{1}{2} \rho\left(v_1^2-v_2^2\right)=P_2 \\ & \Rightarrow \quad P_2=50 \times 10^3+\frac{1}{2} \times 10^3 \times\left(1^2-2^2\right) \\ & \Rightarrow \quad P_2=50 \times 10^3-1.5 \times 10^3 \\ & =48.5 \mathrm{kPa} \\ & \end{aligned}$

Asked in: AP EAMCET 2007

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