Question

Groundwater Civil Engineering

Answer 1

The head loss due to friction in the pipe is 0.522 m, using either Manning's equation or the Hazen-Williams equation.

Manning's equation:

hf = n²L/(R²/3S²) * Q²

where:

hf is the head loss due to friction (m)

n is Manning's roughness coefficient (dimensionless)

L is the pipe length (m)

R is the hydraulic radius (m)

S is the slope of the energy grade line (m/m)

Q is the flow rate (m³/s)

Hazen-Williams equation:

hf = 10.67L/
`(C^1.85 * d^4.865) * Q^1.85`

where:

C is the Hazen-Williams coefficient (dimensionless)

d is the pipe diameter (m)

Given:

Diameter, D = 1 m

Length, L = 300 m

Manning's roughness coefficient, n = 0.013

Hazen-Williams coefficient, C = 100

Solve for:

Head loss due to friction, hf

Manning's equation:

hf = n²L/(R²/3S²) * Q²

hf = 0.013² * 300 / (1² / 3 * 1) * 1²

hf = 0.522 m

Hazen-Williams equation:

hf = 10.67L/
`(C^1.85 * d^4.865) * Q^1.85`

hf = 10.67 * 300 /
`(100^1.85 * 1^4.865) * 1^1.85`

hf = 0.522 m