Answer:
V = 50 ft³/s
H.P = 0.466
Explanation:
Given that
Diameter of the duct, D = 0.3 m
Vacuum Pressure of the duct, Z = 0.025 m
P(w) = pressure of water, 1000 kg/m³
P(a) = pressure of air, 1.22 kg/m³
To find the pressure change we use the formula
ΔP = P(w) * g * Z
ΔP = 1000 * 9.8 * 0.025
ΔP = 245 Pa.
We need the area, do we find that too
A = πd²/4
A = π * 0.3² * 1/4
A = 0.071 m²
Recall the energy equation to be
1/2v² = ΔP/p(a) , so that if we rearrange, we have
v² = 2ΔP/p(a)
v = √(2ΔP/p(a)), on substituting the values, we have
v = √(2 * 245)/1.22
v = √490/1.22
v = √401.64
v = 20.04
The volume flow rate is then equal to
Velocity * Area.
V = 20.04 * 0.071
V = 1.42 m³/s, converting to ft³/s, we have 50 ft³/s
Horsepower output is gotten using
P = ΔP * V
P = 245 * 1.42
P = 347.9 w, converting this to HP, we have 0.466 HP
