Question

Suppose you have a 8.2 cm diameter fire hose with a 3.2 cm diameter nozzle. Calculate the pressure drop due to the Bernoulli effect as water enters the nozzle from the hose at the rate of 40.0 L/s. Take 1.00 × 10^3 kg/m^3 for the density of the water.

Answer 1

Answer:1207.811 KPa

Explanation:

Given

Nozzle and hose are at same level thus

$h_1=h_2$

Applying Bernoulli's equation

$P_1+\frac{1}{2}\rho v_1^2+\rho gh_1=P_2+\frac{1}{2}\rho v_2^2+\rho gh_2$

thus

$P_1-P_2=\frac{1}{2}\cdot rho\left ( v_2^2-v_1^2\right )$

Also discharge (Q)=AV

$v=\frac{Q}{A}$

$P_1-P_2=\frac{1}{2}\cdot rho\left ( \frac{Q^2}{A_2^2}-\frac{Q^2}{A_1^2}\right )$

$P_1-P_2=\frac{1}{2}\cdot rho \left ( 49.729^2-7.573^2\right )$

$P_1-P_2=1207.811 KPa$