Water Resources Engineering

Flow Through Pipes

Darcy–Weisbach friction, major and minor losses and pipe networks — the head losses that size pumps and pipelines.

PART 1

Topic Breakdown & Traps

Flow in a full pipe loses energy to friction. The Darcy–Weisbach equation gives the major loss

h_{f} = \frac{f L V ^{2}}{2 g D}

, where

f

depends on Reynolds number and roughness (Moody chart). Minor losses at fittings, bends and expansions scale with the velocity head

\frac{V ^{2}}{2 g}

. A sudden expansion loses

\frac{( V _{1} - V _{2} ) ^{2}}{2 g}

Darcy–Weisbach (major loss):

h_{f} = \frac{f L V ^{2}}{2 g D}

Discharge:

Q = A V = \frac{π D ^{2}}{4} V

Minor loss:

h_{m} = K \frac{V ^{2}}{2 g}

Sudden expansion:

h_{L} = \frac{( V _{1} - V _{2} ) ^{2}}{2 g}

⚠
Two friction-factor conventions. Darcy $f$ is four times the Fanning $f$ — confirm which the formula expects.
⚠
Diameter, not radius, in Darcy–Weisbach — and $V$ is the mean velocity $Q / A$ .
⚠
Minor losses use the velocity head, so they grow with $V^{2}$ , not $V$ .

PART 2

Q1BASIC1 Mark · NAT

Water flows at

V = 2 m/s

through a

0.2 m

pipe,

L = 100 m

f = 0.02

. The friction head loss is _____ m.

Q2MEDIUM1 Mark · NAT

A pipe of diameter

0.3 m

carries water at

1.5 m/s

. The discharge is _____ m³/s.

Q3HARD2 Marks · NAT

At a sudden expansion the velocity drops from

3 m/s

1 m/s

. The head loss is _____ m.