Question

Air discharge steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in the figure




The inlet and outlet areas of the nozzle are 0.1 $m^2$ and 0.02 $m^2$, respectively. Take air density as constant and equal to 1.2 kg/$m^3$. If the inlet gauge pressure of air is 0.36 kPa, the gauge pressure at point O on the plate is_____ kPa (round off to two decimal places).

• A. 0.375

Answer 1

The correct option is A 0.375
On applying continuity equation,
$m={\rho }_1.A_1.v_1={\rho }_2.A_2.v_2$
$\Rightarrow$ $0.1V_1=0.02V_2$
$\Rightarrow$ $V_2=\frac{10}{2}{V}_1=5V_1$
Now on applying Bernoulli's between sections 1 and 2








$\frac{P_1}{\rho g}+\frac{V_1^2}{2g}+z_1=\frac{P_2}{\rho g}+\frac{V_2^2}{2g}+z_2$
$\Rightarrow \frac{0.36\times {10}^3}{1.21\times 9.81}+\frac{V_1^2}{2g}=\frac{25V_1^2}{2g}$
$\Rightarrow V_1=4.98m/s$
$\Rightarrow V_2=24.89m/s$
On applying Bernoulli's between section 2 and point O
$\frac{P_2}{\rho g}+\frac{V_2^2}{2g}+z_2=\frac{P_O}{\rho g}+\frac{V_O^2}{2g}+z_O$
$P_O=\frac{\rho g.V_2^2}{2g}=\frac{1.21\times (24.89{)}^2}{2}=375Pa$
=0.375 kPa(gauge)