The pressure drop due to the Bernoulli effect is 122,760 N/m² (1.23 bar).
Given:
Diameter of fire hose (d1) = 8.7 cm = 0.087 m
Diameter of nozzle (d2) = 3.1 cm = 0.031 m
Flow rate (Q) = 39 L/s = 0.039 m³/s
Density of water (ρ) = 1000 kg/m³
Calculate the velocity in the fire hose (v1):
A1 = πd1²/4 = π(0.087)²/4 = 0.060 m²
v1 = Q / A1 = 0.039 / 0.060 ≈ 0.65 m/s
Calculate the velocity in the nozzle (v2):
A2 = πd2²/4 = π(0.031)²/4 = 0.0076 m²
v2 = Q / A2 = 0.039 / 0.0076 ≈ 5.13 m/s
Apply Bernoulli's equation:
p1 + 0.5ρv1² = p2 + 0.5ρv2²
where:
p1 is the pressure in the fire hose (unknown)
p2 is the pressure in the nozzle (atmospheric pressure = 0 Pa)
Solve for p1:
p1 = 0.5ρ(v2² - v1²)
p1 = 0.5 * 1000 * (5.13² - 0.65²) ≈ 122,760 Pa
Question:-
(a) What is the pressure drop (in N/m2) due to the
Bernoulli effect as water goes into a 3.1 cm diameter nozzle from a
8.7 cm diameter fire hose while carrying a flow of 39 L/s?