Find the total friction loss in 100 mm diameter G. I. pipe discharging 4 L/s ina total length of 300 m. Assume pipe roughness, ε = 0.20 m. (hint: use the nomogram, use the head loss equation (darcy-weisbach equation) to calculate, hf and moody's diagram to estimate friction factor, f and compare the result.)

friction factor, f = 0.025, hf = 0.9903 m

Explanation:

We are given the following:

Diameter, D = 100 mm = 0.1 m

Rate of discharge, Q = 4 L/s = 0.004 m³/s

Length of pipe, L = 300 m

pipe roughness, ε = 0.2 mm

velocity of pipe, v = ?

From rate of discharge = velocity * area, hence

0.004 = v * (π * (0.1/2) ²) where area = π * (D/2) ²

solving the above expression, we have

v = 0.509 m/s

from Reynold's number = velocity * diameter / dynamic viscosity

i. e Re = V * D / μ

where μ = 10⁻⁶

hence, substituting the values, we have

Re = 0.509 * 0.1 / 10⁻⁶

Re = 50900 and ε/d = 0.2 / 100 = 0.002

from the moody diagram

friction factor, f = 0.025 and I = 300

total friction loss hf = flV² / (2gD)

hf = (0.025 * 300 * 0.509²) / (2 * 9.81 * 0.1)

This evaluates to

hf = 0.9903 m