Question

Consider a flow through a nozzle, as shown in the figure below

The air flow is steady, incompressible and inviscid. The density of air is 1.23 $kg/m^3$. The pressure difference $(p_1-p_{atm}$) is ______kPa (round off to the nearest integer).

• A. 1.52

Answer 1

The correct option is A 1.52
As per given data, ${\rho }_{air}=1.23kg/m^3$

$A_1{V}_1=A_2{V}_2$
$0.2\times V_1=0.02\times 50$
$V_1=\frac{1}{10}\times 50=5m/s$
Applying BE
$\frac{P_1}{w}+\frac{V_1^2}{2g}+z_1=\frac{P_2}{w}+\frac{V_2^2}{2g}+z_2$
$(\because z_1=z_2)$
$\frac{P_1-P_2}{{\rho }_{air}g}=\frac{V_2^2-V_1^2}{2g}$
Pressure difference,
$P_1-P_2=\left(\frac{{50}^2-5^2}{2}\right)\times 1.23$
=1522.125 Pa
1.52 kPa