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Pressure drop is created when a difference in pressure arises between the two points of the fluid carrier network. When the fluid passes through a tube, frictional force takes place. It is because of the resistance that is created in the fluid of the tube. The more is the frictional force in the by plane the less is the pressure drop. While determining the pressure drop formula, J Represents Pressure Drop. The fluid can be either air or water. And it is the quality of the line pressure that determines the pressure drop. When there is absolute friction between different parts of the device, the pressure drop takes place when any instrument is fitted there is always a drop of pressure.
Key terms: Pressure drop, inverse relationship with the pipe diameters, viscosity of the fluid medium
Factors Affecting Pressure Drop
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Some of the factors that affect pressure drop are as follows:
Diameter of the Pipe
The pressure drop has an inverse relationship with the pipe diameters. When the flow of the fluid is restricted within the web by the inner and outer diameters of the pipe, the pressure loss takes place. If the diameter is more the fluid can pass easily through the pipe and it will not get any resistance hence the pressure drop will be below. On the other hand, if the diameter is narrow, it will get resistance from the other side and the fluid will take more time to reach the other side of the pipeline. Therefore, the pressure drop is more.
Pressure drop due to pipe diameter
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Pipe Bend
When the pipes bend, it becomes difficult for the fluid to pass from one side to the other and leads to the loss of energy and data. When the energy is lost inside the pipe, the pressure drop also takes place. Hence there is always a reverse relationship between the pipe surface and the flow of the fluid. If the pipe is straight and there is not much resistance in its shape it will not provide any viscosity issue for the fluid and the energy drop will not take place.
Pressure drop due to pipe bend
Valve Installation
If the valves of the pipe are open, there will be no resistance and hence pressure loss will not take place. If the valves are closed or any one valve is closed it will change the direction of the fluid flow inside the pipe and will lead to pressure loss. When the valves are opened, the fluid can flow freely resulting in no pressure drop. Again if the valves are totally opened but the path for fluid flow is changed consequently, the pressure drop will increase.
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Pressure Drop Formula
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When there is a changing path and a lot of resistance within the pipe, a pressure drop takes place. Previously, many methods were used to calculate the exact energy loss due to such friction but none of them provided exact results. Finally, the fiberglass pipe was used along with the Darcy equation based on which the absolute pressure drop universal formula was determined. With this formula, you can easily get accurate results of pressure drop within the pipe of all diameters.
The Universal Pressure Drop Formula is-
J= fLv2/ 2gD
Where,
J is the Pressure Drop
f is the friction factor used
L is the length or the diameter of the pipe
v is the velocity of the fluid
g is the acceleration of gravity
D is the inner diameter of the tube
This formula also determines the relative roughness of the object depending on the flow of the medium.
Let us understand this equation by a simple example-
Suppose the velocity of the fluid would be 60 meters per second. The outer diameter of the tube is 20 meters and the inner diameter of the same tube is 0.1 meters. If the friction factor is 0.5 then what will be the pressure drop of the fluid?
J= fLv2/ 2gD
Herein,
F= 0.5
L= 20m
V= 60m per sec
g = 9.8m per sec
D= 0.1m
Putting these values on the desired Pressure Drop Formula, it stands out to be
(0.5 × 20 × 602/ 2 × 9.8 × 0.1)
J = 18367.34 pa
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 Pressure Drop or energy loss it is always better to determine the choke friction. If the choke friction is still in circulation, then Pressure Drop is to be calculated after the pipe stands by.
| Example: If the length of the tube is 4m, the inner diameter is 0.5 m and the friction factor is 0.3. Calculate the pressure drop of a liquid having flow of 10 m per sec. It is mentioned that, f = 0.3, L = 4 m, v = 10 m per sec, g = 9.8 m per sec, D = 0.5 m Hence, the Pressure drop formula will be like- J= \(\frac{fLv^{2}} {2_{g}D}\) J= \(\frac{0.3X4X10{^2}}{2X9.8X0.5}\) J=12.24Pa. |
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Things to Remember
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- In the Darcy equation, mostly if you come across K, it means the height, roughness of the surface, or the diameter of the pipe. Therefore, it is easy to get the exact data using this equation.
- Always remember that the resistance differs from the viscosity of the fluid medium.
- Pressure Drop is no different than the friction loss of the fluid which is again 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. The more the barrier and shape differences, the more the Pressure Drops and vice-versa.
- Record the choke friction at 25-28 strokes/m to get accurate results.
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Important PYQs Related to This Chapter
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Sample Questions
Ques. Explain the inverse relationship between the Pressure Drop of the fluid and the diameter of the pipe? (5 marks)
Ans. The flow rate of the fluid and the fluid properties are some of the important factors on which the calculation of pressure drop 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 or gets a rough and irregular surface, it gets the maximum resistance increasing the level of pressure drop. It was only seen in the experiment that the square corners are getting more proportional resistance. Hence there is an inverse relationship between the diameter of the pipe and the Pressure Drop of the fluid.
Ques. What do you mean by gravitational constant g? (5 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 pressure drop 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? (5 marks)
Ans. The common friction factors that can be used for the experimentation of pressure drop are asbestos cement, concrete tube, copper tube, glass tube, lead pipe, PVC pipe, teen tube, wood Stave. For experimenting with a pressure drop of the fluid, 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. Define Pressure Drop. (3 marks)
Ans. When a difference in pressure arises between the two points of the fluid carrier network, it is called pressure drop. When the fluid passes through a tube, frictional force takes place. It is because of the resistance that is created in the fluid of the tube. The more is the frictional force in the by plane the less is the pressure drop. While determining the pressure drop formula, J Represents Pressure Drop.
Ques. What are the factors affecting the Pressure Drop of the fluid? (3 marks)
Ans. The factors affecting the Pressure Drop of the fluid are as follows:-
- When the flow of the fluid is restricted within the web by the inner and outer diameters of the pipe, the pressure loss takes place. If the diameter is more the fluid can pass easily through the pipe and it will not get any resistance hence the pressure drop will be below and vice-versa.
- When the pipes bend, it becomes difficult for the fluid to pass from one side to the other leading to the loss of energy and data. If the pipe is straight and there is not much resistance in its shape it will not provide any viscosity issue for the fluid and the energy drop will not take place.
- When the valves are opened, the fluid can flow freely resulting in no pressure drop. Again if the valves are totally opened but the path for fluid flow is changed consequently, the pressure drop will increase.
Ques. Determine the universal formula of Pressure Drop. (5 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.
J= fLv2/2gD
Where,
J is the Pressure Drop
f is the friction factor used
L is the length or the diameter of the pipe
v is the velocity of the fluid
g is the acceleration of gravity
D is the inner diameter of the tube
Ques. What does h1 represent while calculating the Pressure Drop? (3 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. Suppose the velocity of the fluid would be 10 meters per second. The outer diameter of the tube is 4 meters and the inner diameter of the same tube is 0.5 meters. If the friction factor is 0.3 then what will be the pressure drop of the fluid? (consider the universal value of g) (3 marks)
Ans. J= fLv2/2gD
Herein,
F= 0.3
L= 4 m
V= 10 m per sec
g = 9.8m per sec (universal value)
D= 0.5 m
Putting these values on the desired Pressure Drop Formula, it stands out to be
( 0.3×4×102/2×9.8×0.5)
= 12.24 pa
Ques. Consider all the factors of the flow constant then what will be the effect on the Pressure Drop if the fluid flow is constant? (2 marks)
Ans. The possibility varies with different experiments. In different fluids the reaction is different. If you place the equation accordingly the results will vary. If the fluid pressure is incompressible, the pressure drop will increase at a good pace. Again, if the fluid flow is constant without getting any resistance then the pressure drop will reduce accordingly.
Ques. In most of the pipes why the Pressure drop is constant? (3 marks)
Ans. When the fluids pass through a pipe, they face resistance from the walls of the pipe. Darcy's formula is used to get a combined answer based on the resistance and the diameter of the pipe. Once the diameter and the valves are set, it determines the flow of the fluid and the pressure drop. At the initial stage when the pressure drop is measured, consequently it does not change because the flow of the fluid does not change. If there is any further resistance in the fluid flow because of the change of the size or valve placements, then the pressure drop will change otherwise it will remain constant throughout.
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