Step-by-step explanation:
The pressure drop can be calculated using the Darcy-Weisbach equation:
ΔP = (f * L * V^2) / (2 * g * D)
where:
ΔP = Pressure drop (psi)
f = Darcy friction factor
L = Length of pipe (ft)
V = Velocity of fluid (ft/s)
g = acceleration due to gravity (32.2 ft/s^2)
D = Inner diameter of pipe (ft)
To calculate the velocity, use the equation:
V = Q / A
where:
V = Velocity (ft/s)
Q = volumetric flow rate (ft^3/s)
A = cross-sectional area of pipe (ft^2)
To convert volumetric flow rate from gpm to ft^3/s:
Q = 50 gpm * 0.002228 ft^3/s/gpm
The diameter of the 2" Schedule 40 commercial steel pipe can be found from pipe dimensions charts and is approximately 0.154 ft.
The cross-sectional area can be calculated as:
A = π * (D/2)^2
Plugging in the values:
V = (50 * 0.002228) / (π * (0.154/2)^2) = 24.7 ft/s
ΔP = (f * 50 * 24.7^2) / (2 * 32.2 * 0.154)
The value of the friction factor, f, can be estimated using the Moody diagram or calculated using a more complex equation such as the Colebrook-White equation.
Note: This is a simplified calculation and does not account for all factors that could affect pressure drop such as changes in pipe elevation, fittings, and valves.