## Darcy Weisbach Equation for Friction Loss

**Darcy Weisbach Equation for Friction Loss** Assignment Help | **Darcy Weisbach Equation for Friction Loss** Homework Help

# Darcy-Weisbach Equation for Friction Loss

Consider a uniform horizontal pipe having steady flow. Let fluid mass between section 1-1 and 2-2 as shown in.

Let A = Area of the pipe

L = Length of pipe between

1-1 and 2-2

d = diameter of the pipe

P

V1 and V2 = velocity at section 1-1 and section 2-2, respectively.

Applying Bernoulli’s equation between 1-1 and 2-2,

But Z

V

P

h

Where h

Experimentally it was found by Froude that the frictional resistance is given by,

Frientional resistance = Frictional resistance per unit wetted are a per unit velocity x Wetted

are x Velocity

F = f ‘ x π d L x V

F = f ‘ P L V

Since the velocity of flow is constant from section 1-1 to 2-2.

Net force in the direction of flow = 0

P

F = (P

Equating Equations

f P L V

P

Now, equating Equations

γ. h

h

Where hydraulic radius = P/A = wetted perimeter / Area = π d / πd

Putting f'/ρ= f/2 were f = coefficient of friction.

f' f ρ/2

h

This is Darcy Weisbach equation for frictional loss

Sometimes Equation is written as,

h

Where f = friction factor = 4 x coefficient of friction

But V = Q/A = 4Q / π d

h

h

For more help in

Let A = Area of the pipe

L = Length of pipe between

1-1 and 2-2

d = diameter of the pipe

P

_{1}and P_{2}= pressure intensity at section 1-1 and section 2-2, respectively.V1 and V2 = velocity at section 1-1 and section 2-2, respectively.

Applying Bernoulli’s equation between 1-1 and 2-2,

But Z

_{1}= Z_{2}since the pipe is horizontalV

_{1}= V_{2}since the pipe of uniform diameter,P

_{1}/ γ P_{2}/ γ + h_{f}h

_{f }= P_{1 }- P_{2}/ γWhere h

_{f}= head loss due to frictionExperimentally it was found by Froude that the frictional resistance is given by,

Frientional resistance = Frictional resistance per unit wetted are a per unit velocity x Wetted

are x Velocity

^{2}F = f ‘ x π d L x V

^{2}F = f ‘ P L V

^{2}Since the velocity of flow is constant from section 1-1 to 2-2.

Net force in the direction of flow = 0

P

_{1}A – P_{2}A – F = 0F = (P

_{1}– P_{2}) AEquating Equations

f P L V

^{2}= (P_{1}- P_{2}) AP

_{1}- P_{2}= f' P L V^{2}/ ANow, equating Equations

γ. h

_{f }= f' P L V^{2}/ Ah

_{f }= f' / γ x P/A X LV^{2}Where hydraulic radius = P/A = wetted perimeter / Area = π d / πd

^{2}/ 4 = 4/dPutting f'/ρ= f/2 were f = coefficient of friction.

f' f ρ/2

h

_{f }= 4 f L V^{2}/ 2g dThis is Darcy Weisbach equation for frictional loss

Sometimes Equation is written as,

h

^{f}= f L V^{2}/ 2g dWhere f = friction factor = 4 x coefficient of friction

But V = Q/A = 4Q / π d

^{2}h

_{f}= fL / 2g d (4q / πd^{2})^{2 }= 16 f L Q^{2}/ 2g π^{2}d^{3}h

_{f}= f L Q^{2}/ 12.1d^{3}For more help in

**Darcy-Weisbach Equation for Friction Loss**click the button below to submit your homework assignment