Question

The flow of water in a horizontal pipe is streamline. At a point in the tube where its cross-sectional area is $10c{m}^2$, the velocity of water and pressure are 1m/s and $2\times {10}^3$ pascal, respectively. The pressure of water at a different point, where the cross-sectional area is $5c{m}^2$ will be:

• A. $2000$ Pascal.
• B. $1000$ Pascal.
• C. $250$ Pascal.
• D. $500$ Pascal.

Answer 1

The correct option is D $500$ Pascal.

Using equation of continuity, we can find the velocity at another point. we have
$a_1{v}_1=a_2{v}_2\Rightarrow 10\times 1=5\times v_2\Rightarrow v_2=2m/s$

According to Bernoulli's theorem, for water at the same height
$\Delta P=\frac{\rho (v_1^2-v_2^2)}{2}\Rightarrow \Delta P=\frac{1000\times (1^2-2^2)}{2}=-1500Pa\Rightarrow P_2-P_1=-1500Pa\Rightarrow P_2-2000=-1500Pa\Rightarrow P_2=500Pa$