## Chezys Formula for Loss of Head due to Friction

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# Chezy’s Formula for Loss of Head due to Friction

Consider uniform horizontal pipe as shown in and Equation derived in Darcy-Weisbach equation.

Where is, h

We know, hydraulic radius is the ratio of area of flow to wetted perimeter. It is denoted by ‘m’.

m = A/P = π/4d

P/A = 1/m

put value of P/A in Equation,

h

V

V = √ γ / f'. h

Consider √ γ / f' = C i.e. Chezy’s constant and

h

Put the above value in Equation,

V = C√m i

This is known as Chezy’s formula.

Relation between the freiction factor f and the chezy’s constant C:

Head loss due to Darcy Equation,

hf = fLV

From Chezy’s Equation, V = C√m i

Where, m = d/4, I = hf/L put in Equation,

V = C √m i

Squaring both side, V

h

Equate Equation

f LV

f = 8g / C

This is the required relation between Darcy’s coefficient and Chezy’s Constant.

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Where is, h

_{f}= f’/ γ. P/A X L V^{2}We know, hydraulic radius is the ratio of area of flow to wetted perimeter. It is denoted by ‘m’.

m = A/P = π/4d

^{2}/ πd = d/4P/A = 1/m

put value of P/A in Equation,

h

_{f}= f’/ γ. 1/m. L V^{2}V

^{2 }= h_{f}. γ.m / f’.LV = √ γ / f'. h

_{f }/ L. mConsider √ γ / f' = C i.e. Chezy’s constant and

h

_{f }/ L = I i.e. loss of head per unit length of pipe.Put the above value in Equation,

V = C√m i

This is known as Chezy’s formula.

Relation between the freiction factor f and the chezy’s constant C:

Head loss due to Darcy Equation,

hf = fLV

^{2}/ 2gdFrom Chezy’s Equation, V = C√m i

Where, m = d/4, I = hf/L put in Equation,

V = C √m i

Squaring both side, V

^{2}= C^{2}x d/4 x h_{f}/ Lh

_{f}= 4V^{2}L / C^{2}dEquate Equation

f LV

^{2}/2gd = 4V^{2}L/C^{2}df = 8g / C

^{2}This is the required relation between Darcy’s coefficient and Chezy’s Constant.

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