Friction Loss Formula

The flow of fluid through a pipe is resisted due to the viscous shear stresses within the fluid and the turbulence. These turbulences occur along the internal pipe wall, which will be dependent on the roughness of the pipe material. Friction losses are a complex function of the system geometry and it corresponds to the fluid properties and the flow rate in the system. By observation, we may see that this loss is roughly proportional to the square of the flow rate in most engineering flows. This topic will deal with friction loss concepts and friction loss formula with examples. Let us learn it!

What is Friction Loss?

Friction may be observed as the resistance required for moving a body through the external surface. But the friction loss is related to the flow of liquid through some pipe. Thus, it is a kind of energy loss due to the friction inside the tube. It is therefore related to the velocity and viscosity of the fluid. Friction loss can be computed as \(h_l\) as friction loss is nothing but the energy loss. This resistance is termed as pipe friction and is measured in meters head of the fluid. Many types of research have been carried out to establish various formulae to calculate this loss.

The Darcy formula or the Darcy-Weisbach equation mainly tend to be referred for this computation. And is now accepted as the most accurate pipe friction loss formula. Although it is more difficult to calculate and use than other friction loss formulas, with the introduction of computers, it has become the standard equation for hydraulic engineers.

Formula for Friction Loss

Friction loss formula is: \(h_l = f \times \frac {L}{D} \times \frac {v^2}{2g}\)

Where,

• f is the friction factor
• L is the length of the pipe
• D is the inner diameter of the pipe
• V is the velocity of the liquid
• g is the gravitational constant
• \(h_l\) is the friction lost

Reynolds Number is the basic dimensionless group in viscous flow. Velocity times Length Scale divided by Kinematic Viscosity. Relative Roughness is related to the height of a typical roughness element to the scale of the flow.

Solved Examples for Friction Loss Formula

Q.1: Find out the friction loss, if the inner diameter and length of the pipe are 0.3 m and 30 m respectively. Also, the friction factor and velocity of the liquid are 0.4 and 25 m per sec?

Solution: Given parameters,

• Length of the pipe, L = 30 m
• internal diameter, D = 0.3 m
• velocity of the liquid, v = 25 m per sec
• friction factor, f = 0.4
• \(g = 9.8 m per sq sec^2\)

Now, friction loss formula is,

\(h_l = f \times \frac {L}{D} \times \frac {v^2}{2g} \\\)

\(= 0.4 \times \frac {30}{0.3} \times \frac {25^2}{2 \times 9.8} \\\)

\(= 1275.51\; m\)

Q.2: Determine the friction loss if the friction factor is 0.3 and velocity of the flow is 50 m per sec. Given length of the pipe is 20 m, inner diameter 0.5 m. Use friction loss formula.

Solution: Given parameters are,

• v = 50 m per s,
• L = 20 m,
• D = 0.5 m,
• f = 0.3 and
• Gravitational constant, \(g = 9.8 m per s^2,\)

The friction loss formula is,

\(h_l = f \times \frac {L}{D} \times \frac {v^2}{2g} \\\)

\(= 0.3 \times \frac {20}{0.5} \times \frac {50^2}{2 \times 9.8} \\\)

\(= 1530.61 \; m\)