Question

At a point $P$ in a water pipe line the velocity is $1m{s}^{-1}$ and the pressure is $3\times {10}^{5}pa$ . At another point $Q$, the area of cross section is half that of at P and the pressure is $5\times {10}^{5}Pa$ . The difference of heights between $P$ and $Q$ in metre is : ( $g=10m{s}^{-2}$)

• A. $10.5$
• B. $20.15$
• C. $4.5$
• D. $0$

Answer 1

The correct option is B $20.15$

Applying continuity equation across P and Q

$A_2{V}_2=A_1{V}_1$

$\Rightarrow V_2=2m{s}^{-1}$

Using bernouillis theorem across point P and Q,
$3\times {10}^5+\frac{1}{2}\times 1000\times {\left(1\right)}^2+\lambda g{h}_1=\lambda g{h}_2+\frac{1}{2}\times 1000\times 4+5\times {10}^5$
$\Rightarrow h_1=h_2=\frac{200+5\times {10}^5-3\times {10}^5-500}{\lambda g}$
So,
Difference in height $=20.15m$