Water Resources Engineering

Fluid Mechanics & Flow

Continuity, Bernoulli, hydrostatics and Manning's open-channel flow — the hydraulics fundamentals.

PART 1

Topic Breakdown & Traps

Continuity conserves mass:

Q = A v

is constant along a streamtube. Bernoulli conserves energy along a streamline. Hydrostatic pressure rises linearly with depth,

p = γ_{w} h

. In open channels, Manning's equation relates velocity to slope and hydraulic radius.

Continuity:

Q = A_{1} v_{1} = A_{2} v_{2}

Bernoulli:

\frac{p}{γ} + \frac{v ^{2}}{2 g} + z = const

Hydrostatic pressure:

p = γ_{w} h

Manning:

v = \frac{1}{n} R^{2/3} S^{1/2}

Reynolds number:

R e = \frac{v D}{ν}

(

< 2000

laminar,

> 4000

turbulent).

⚠
Bernoulli = energy conservation, not momentum. It needs steady, incompressible, inviscid flow along a streamline.
⚠
**Hydraulic radius $R = A / P$ **, not the geometric radius.
⚠
Gauge vs absolute pressure. $p = γ_{w} h$ gives gauge pressure.

Hydraulics and Fluid Mechanics (including Hydraulic Machines) — P.N. Modi & S.M. Seth

PART 2

Q1BASIC1 Mark · NAT

Water flows through a pipe of area

0.5 m^{2}

2 m/s

. The discharge is _____ m³/s.

Q2MEDIUM1 Mark · NAT

The gauge pressure at

5 m

depth below a free water surface (

γ_{w} = 9.81 kN/m^{3}

) is _____ kPa.

Q3HARD2 Marks · NAT

Using Manning's equation with

n = 0.013

R = 0.5 m

and

S = 0.001

, the mean velocity is _____ m/s.