Commonly Used Formula in Hydraulics

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Darcy Weisbach formula
Darcy Weisbach formula which is valid for laminar or turbulent flow in all fluids is one of the most commonly used formula for determining the head loss.

h_f=[fLV²]/2gD

where
h_f=head loss due to friction, ft (m)

f= friction factor

L =length of pipe, ft (m)

D= diameter of pipe, ft (m)

V =velocity of fluid, ft/s (m/s)

g =acceleration due to gravity, 32.2 ft/s2 (9.81 m/s2)

Chezy Formula

This Equation holds got for head loss in conduits and gives good results for high Reynolds numbers:
V=C(RS)^1/2

where
V=velocity,ft/s(m/s)

C=coefficient depending on surface roughness of conduit
S=slope of energy grade line or head loss due to friction of conduit
R=hydraulic radius,ft(m)
Generally R=Area/wetted perimeter

Manning’s Formula
According to this

C=1.486R^1/6/n

where
n=coefficient depending on surface roughness.Now with this vaue of R=D/4 we can calculate V and Q.

Hazen Williams Formula
This is one of the most widely used formula and is given below:

V=1.318C₁R^0.63S^0.54

R= hydraulic radius, ft (m)

S= head loss due to friction, ft/ft (m/m) of pipe

D= diameter of pipe, ft (m)
L= length of pipe, ft (m)
Q= discharge, ft³/s (m³/s)
hf =friction loss, ft (m)

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