Question

A horizontal pipeline carries water in a streamline flow. At a point where the cross-sectional area is $10{\text{cm}}^2$, the water velocity is $1{\text{ms}}^{-1}$ and pressure is $2000\text{Pa}$. The pressure of water at another point where the cross sectional area is $5{\text{cm}}^2$, is:

• A. $200\text{Pa}$
• B. $400\text{Pa}$
• C. $500\text{Pa}$
• D. $800\text{Pa}$

Answer 1

The correct option is C $500\text{Pa}$


Let the pressure be $P$ at the second point and let velocity be $v_2=v$
Applying equation of continuity:
$A_1{v}_1=A_2{v}_2$
$10\times 1=5\times v$
$\Rightarrow v=2{\text{ms}}^{-1}$
Apply Bernoulli's theorem at both the points,
$P_1+\frac{1}{2}\rho v_1^2+\rho gh=P_2+\frac{1}{2}\rho v_2^2+\rho gh$
[$h=$ constant]
$\Rightarrow 2000+\frac{1}{2}\times 1000\times 1^2=P+\frac{1}{2}\times 1000\times 4$
$\therefore P=500\text{Pa}$