Friction Loss Formula & Darcy Weisbach Equation

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Friction Loss is the pressure that takes place in the pipe full of fluids. If the height of the water level increases to a certain level and the viscosity of the fluid takes place near the pipe, frictional loss occurs. In internal combustion it is called power lost when the friction of two surfaces takes place. The air and water are called fluid in friction because they cannot take any shape. Air and water both provide resistance. The frictional force that takes place due to the force of the water is called drag. 

Keyterms: Friction, Pressure, Water level, Fluids, Viscosity, Resistance, Air, Power, Liquid, Gas


Factors Affecting Fluid Friction

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Some of the factors that affect Fluid friction are as follows:

Nature of the Fluid

The nature of the liquid or gas decides the type of fluid friction. We can understand this with a simple example. 

Fluid Friction

Fluid Friction

Suppose X and Y are the two objects. The first time, X moves towards Y in the air and covers the journey in 5 mins. Again, X moves towards Y in water and now it takes around 10 mins to complete its path. This time difference is the resultant of the fluid friction. Water is thicker than air. So, water provides more resistance to object X to complete its journey. And the resistance gives rise to or increases the Fluid Friction. Hence, the higher the viscosity of the fluid medium, the higher the resistance of the fluid. 

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Speed of the object

Speed of the travelling object also decides the speed of the Fluid Friction. The more the speed of the object, the more the fluid friction. 

Example: If a car travels at 100km/hr and the same car travels at 50km/hr, the less-speed car will generate less fluid friction.

Shape of the object

Another factor deciding the fluid friction is the Shape of the object. The shapes are decided accordingly to reduce the level of fluid friction. This is called streamlining. Streamlining reduces Fluid Friction.

Shape of the object affects fluid friction

Shape of the object affects fluid friction

Example- An airplane is shaped like an oval so that it does not get much resistance from the air. If it were square-shaped, then the corners of the box would have received more resistance resulting in a more level of fluid friction. 

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Fluid Friction Formula

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Fluid friction formula is given by,

[Friction Loss Coefficient* (flow rate/100)2 x hose length/ 100]

It is represented as:

FL= C x (Q/100)2 x L/100

Where,

FL= Friction Loss

C= friction Loss Coefficient

Q= Flow rate

L= hose length

Let us understand through an example- 

Example: Determine the friction loss for a 100-foot 1.75-inch fire hose that flows at 250GPM of water.

Coefficient of the friction loss is 1.75” is 15.5

Ans. Q= 250 GPM

L= 100ft

So, FL= [C*(Q/100)2*L/100

FL = 15.5*(250 GPM/100)2*100ft/100

FL = 96.875 PSI

The Darcy equation is used to determine this formula. After the final equation was set, it was seen that this formula matches the best to determine the friction loss of the fluid. Hydraulic engineers generally use this equation to determine such results. 

Herein, 

FL= f x L/D x v2/2g

Where,

f= friction

L= pipe diameter

D= inner length of the diameter of the pipe

g= gravitational constant

h= friction lost

This formula determines the relative roughness of the object depending on the flow of the medium. 

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Let us understand this equation by an example-

Example: Suppose the friction is 0.3, the velocity of the medium is 50 m/sec and the outer and the inner diameter of the pipe is 20m and 0.5m. What is friction loss?

Ans. 

FL= f x L/D x v2/2g

v= 50 m/sec

L= 20m

D= 0.5m

f= 0.3

g= 9.8 m/s2

So, 0.3 x 20/0.5 x 502/(2 x 9.8)

FL= 1530.61m

Note that the pressure of the water depends on the depth of the water. The choke can take place in the diameter of the pipe. Before generating the final results of the friction loss it is always better to determine the choke friction. If the choke friction is still in circulation, then friction loss is to be calculated after the pipe stands by. 

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Things to Remember 

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  • In this Darcy equation, mostly if you come across K, it means the height, roughness of the surface, or the diameter of the pipe. 
  • Always remember that the friction level differs from the viscosity of the fluid medium.
  • Friction Loss is nothing but the loss of energy that depends on the diameter of the pipe and the density of the medium. It takes place inside the length of the object.
  • The gravitational constant is mostly 9.8m/s as it is considered the universal value. 
  • The results will vary with the movements of the fluids.
  • Record the choke friction at 50 strokes/m to get accurate results.

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Sample Questions 

Ques. Define Fluid Friction. (3 marks)

Ans. The pressure that takes place in the pipe full of fluids is called Friction Loss. If the height of the water level increases to a certain level and the viscosity of the fluid takes place near the pipe, friction loss generates. It can take place in any medium whether air, water, or surface. When on the surface it is termed as a loss of energy and when in air and water, then it is called Fluid Friction.

Ques. Determine the universal formula of Fluids Friction. (3 marks)

Ans. The Darcy equation is used to determine this formula. Previously, many other equations were tried to determine the fluid friction but everything failed to reach the exact equation. Then, it was seen that Darcy's equation could determine the exact loss of energy inside the pipe. So, it is set as the Universal Equation.

FL= f x L/D x v2/2g

where,

f= friction

L= pipe diameter

D= inner length of diameter of the pipe

g= gravitational constant

h= friction lost

Ques. What are the necessary observations in the flow rate and the fluid properties when the friction losses are calculated? (3 marks)

Ans. The flow rate of the fluid and the fluid properties are some of the important factors on which the calculation of friction loss depends. While the experiment is carried out to determine such, it is observed that the loss is almost proportional to the flow rate of the fluid. The engineers noticed that on the surface this loss is found to be exact but on the water, all air gets diverted. So absolute formulas are used to generate the final result of friction loss. When the shape of an object does not match with the fluid medium, it gets the maximum resistance increasing the level of fluid friction. It was only seen in the experiment that the square corners are getting more proportional resistance.

Ques. What is the h1 friction loss formula? (2 marks)

Ans. H1 is the symbol representing energy loss. It is calculated in meters and it takes place inside the pipe. The inner and the outer diameter of the pipe determines the final loss of data. The energy loss means the loss of data. Therefore before determining the final result of the experiment and how much data can be lost if the medium is used further, the experiments are conducted.

Ques. What are the necessary factors determining fluid friction? (5 marks)

Ans. The factors determining the fluid friction are as follows:

  • The nature of the water decides the types of fluid friction. We can understand this with a simple example. 
  • The speed of the traveling object also decides the speed of the Fluid Friction. The more the speed of the object, the more the fluid friction.
  • Another factor deciding the fluid friction is the Shape of the object. The shapes are decided accordingly to reduce the level of fluid friction. This is called streamlining. Streamlining reduces Fluid Friction.

Ques. What do you mean by gravitational constant g? (2 marks)

Ans. The gravitational constant is the acceleration of the gravity of the earth. It is determined by the sea level surface of the earth. The universal gravitational constant is considered to be 9.8 m/s. While calculating the friction loss gravitational constant is required. The value of g depends on the location where the experiment takes place. The density of the medium plays a big role while determining the gravitational constant. but to avoid the values mismatch and regular data loss, the universal value is taken to determine the formula.

Ques. What are the common friction factors? (2 marks)

Ans. The common friction factors that can be used for the experimentation of friction loss are asbestos cement, concrete tube, copper tube, glass tube, lead pipe, PVC pipe, teen tube, wood Stave. For experimenting with fluid friction, such pipes are good; the roughness of the internal surface can be determined. Where the internal surface is different from the external surface, those materials are used for experimenting. The C value will determine the roughness of the surface and thus these are some of the factors that can be used to build the deposits.

Ques. How to rely on the value of the Friction factor, C? (2 marks)

Ans. The value of C can vary. It can be as low as 80 and can go up to 130 as the higher value. The value of the C depends on the material of the pipe used, the density of the fluid, and pipe size. Although fluid friction can be calculated on both the water and air, water shows accurate results. The other medium provides inaccurate results where the value of the C varies to a larger extent. The head loss in the feet of water also varies because of this reason.

Ques. Suppose the hose is 300 GPM and the Friction loss of 80 PSI is 2 inches. Determine the length of the pipe. (2 marks)

Ans. Q= 300 GPM

FL= 80PSI

FL= C*(Q/100)2*L/100

Putting the above values in the formula

The length of the pipe is 111.11ft.

Ques. Suppose the inner and the outer diameter of a pipe are 0.3m and 30m. The friction factor is 0.4 and the velocity of the medium is 25m/s. Determine the Friction loss. (3 marks)

Ans. Length of the hose is 30m (L)

Velocity (v)= 25m/s

Friction Factor (f)= 0.4

Universal gravitational constant (g)= 9.8/s

h1= f*L/D*v2/2g

Putting the above values in the formula 

h1 or energy loss is 1275.51m

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