Question

Fill in the blanks.
A horizontal pipeline carries water in streamline flow. At a point along the pipe, where the cross-sectional area is $10{cm}^2$, the water velocity is $1{ms}^{-1}$ and the pressure is $2000Pa$. The pressure of water at another point where the cross-sectional area is $5{cm}^2$ is _______ $Pa$ ( density of water $={10}^{3}kg{m}^{-3}$ )

Answer 1

As we know,

$a_1{v}_1=a_2{v}_2$

ATQ,

$a_1=10c{m}^2={10}^{-3}{m}^2$

$v_1=1m/s=1m/s$

$a_2=5c{m}^2=5\times {10}^{-4}{m}^2$

$\Rightarrow v_2=\frac{{10}^{-3}\times 1}{5\times {10}^{-4}}=2m/s$

Now, from Bowneil's theorem we get

$P_1+\rho \frac{v_1^2}{2}+\rho g{h}_1=P_2+\rho \frac{v_2^2}{2}+\rho g{h}_2$

ATQ, $h_1=h_2$

$\Rightarrow P_2=P_1+\frac{\rho }{2}(v_1^2-v_2^2)$

$=2000+\frac{1000}{2}(1-4)$

$=2000-1500$

$P_2=500Pa$