Sample Paper: “Pipe Flow and Head Loss”


Water flowing in a pipe at no externally induced pressure will progressively lose strength throughout the pipe. This is owing to the natural effects of friction. Friction refers to the force that resist relative motion, it results when two bodies contact while in motion. In this case, the water inside the pipe is in motion and is therefore likely to face experience some relative resistance of the stagnant pipe. The result is therefore a force that progressively reduces the strength and the outward pressure of the water at the other end of the pipe. Just as is the case with other scientific factors, the amount of friction that the water experiences while in the pipe depends on a number of facts some of which include the roughness of the interior of the pipe.

A rougher surface provides greater resistance to the water flowing inside the pipe since it has a grip point all of which resist the free flow of the water. Another factor is the length of the pipe. A long pipe has a steady and long contact with the water flowing it. This implies that the water progressively tries to counter the friction thereby experiencing increased resistance, which progressively reduces the pressure with which it flow. The final factor is the diameter of the pipe. A wider pipe allows more water to pass through thereby experiencing less contact with the walls of the pipe thereby experiencing smaller amount of friction. In conducting an experimental study of the effects of friction on the flow of water inside a pipe, the researcher therefore considers all the pertinent factors and ensures the he uses standardized pipes and considers the three elements discussed above.


The research considers all the three factors thereby providing a standard base upon which to measure the three. Additionally, the research is repeated in different pipes with different but standardized features as a means of providing a control to the experiment. After measuring all the factors of the pipe and the amount of water flowing in the pipe at any one moment, the following become evident.

Diameter of pipe Volume of water Average flow time Friction factor Mass of water
0.0162 M 0.04 87.5 0.0278 40
0.0162 M 0.02 73.5 0.0295 20

The results above are from the observation of specific parts of both the pipe and the water flowing in it. The diameter of the pipe varies while the length of the pipe stays constant. This therefore measures the different volumes of water capable of passing through the different pipes at any time. This is in an attempt of investigating the role that the diameter of the pipe plays in determining the amount of friction that the water experiences inside the pipe. In doing this, the roughness of the internal surface is kept constant thereby ensuring that all other factors apart from the diameter stays constant.

In the experiment therefore, water is let into the transparent pipe at one end and times on its flow to the other end of the pipe tilted at the same angle. The tilting angle determines the force of gravity, which is arguably an external factor. The factor therefore requires accurate monitoring to ensure that the two pipes experience a similar amount of the gravitational force.
The table below show the relationship between the kinematic viscosities to the diameters of the pipes in the different pipes as the water flows along the tube. Kinematic viscosity refers to the systematic drag that the liquids experience during the flow. As liquids flow down a tube, they gather momentum owing to the rate of the acceleration. In this context, the acceleration is the gravitational flow. Just as any other form of acceleration, this requires a consistent assessment to ensure that both the pipes have similar inclinations and therefore experience similar gravitational acceleration.

Diameter of pipe Volume of water Kinematic Viscosity Friction factor
40 0.04 0.77 (m2/s) 0.0278
20 0.02 0.462 (m2/s) 0.0295

The diameters of thee pipes helps determine the surface area of the pipes. This coupled with te constant length, the volume of the water in each pipe results. With the volume of the water and the universal density of the liquid, it thus becomes possible to determine the mass of the water that each pipe carries along its length. Additionally, the gradient of the inclination of the pipes help determine the rate of acceleration in the pipes a feature that therefore makes it possible to calculate the frictional force that the water experiences in the two pipes. In addition to the volume of the water in the pipes owing to the different pipe diameters, the temperatures of the booth the water and the pipes are important in determining the frictional force in the pipes.

This therefore dictates that the temperature of the pipe is similar to prevent any disparity in the experiment. The experiment of either the water or the pipe expands the pipe relatively thereby creating a bigger diameter than the calculated. The increase in the diameter of the pipe results in the increase of the water volume in the pipes a fact that impairs the effectiveness of the experiment. The concepts of expansion and contraction therefore become pertinent in conducting the experiment since it affects the outcome of the results .for this reason therefore, the research ensures constant room temperature and similar temperature of both the water and the respective pipes.


The angle of inclination aids in calculating the rate of acceleration in the pipe. The gradient of the inclination is the acceleration and is always constant all through the pipe. With the two, a multiplication of the mass and the acceleration results in the determination of the kinematic viscosity. From the computation of the above elements, the result depicts that the bigger pipe has a bigger kinematic viscosity than the smaller one. This is natural and expected owing to the fat that a bigger pipe accommodate more water than the smaller one. This implies that the water in the pipe with a wider diameter has greater mass than that in the smaller pipe thereby having more momentum than the water in the smaller pipe. This explanation alludes that the water in the bigger pipe experiences smaller amount of friction, therefore travel faster, and has more pressure ate the end of the pipe than the water traveling in the smaller pipe.
From the result, it becomes evident that the lighter pipe experiences more friction that the heavier pipe. The reasons for such occurrence is relative and arise from the amount of water that the two diameters convey. The bigger pipe carries more water than that the smaller one. From the experiment, it carries twice the mount of water the smaller pipe carries since the mass of its water twice that of the other pipe. Water has a density of one kilogram per meter’s cube. With such an understanding, it is obvious that a volume of 0.04m^3 equals to a mass of 0.04Kg while the volume of 0.02m^3 equals a mass of 0.02Kg. The conversion of the volume of water into quantifiable mass pipes the preliminary explanation for the difference in the friction that the two pipes exhibit.

By multiplying the mass to the acceleration, one determines the momentum of the water flowing in the pipe. Momentum in this case is equivalent to the force with which the water travels while inside the different pipes. A stronger force, which obviously results from the bigger pipes, has the ability to cancel out the effects of pressure thereby resulting in a faster flow of water. The relative difference in the speeds of water in the two pipes therefore arises from the relativity in the diameters of the pipe. The diameters affect the volume of the water thereby influencing the mass of the water inside the pipe at any moment.

Kinematic viscosity is important in conducting the presence since every action force reacts in a similar reaction force. This implies that the pipes must resist the pressure from both the water and the gravitational pull. By sustaining the two, the walls of the pipe exert equal amount of pressure thereby resisting the water. Kinematic energy is the action force in this context and it cancels out with the resistance from the pipe. However, the pipes produce more energy to resist the pressure thereby resulting in the systematic frictional force. From the diameter and the length of the two pipes, it becomes possible to calculate the volumes of water in each of the pipes. With the volume and the provisional density of fresh water, it is additionally easier to calculate the mass of the water that passes at every point in the pipe.


In retrospect, a pipe with smaller diameter has a smaller volume thereby carrying smaller amount of water compared to any pipe with a bigger diameter. The force of free fall, which accelerates falling particles, is always more on heavier particles a factor that therefore gives the bigger pipe enough force to counter the friction of the pipe. With a greater gravitational drag, the water in the bigger pipe is able to counter friction and therefore travel faster through the pipe than the water in the smaller pipe. The diameter of the pipes in the above experiment determine the difference in the volume of water that each of the liquid experience. It therefore determines the difference in masses of the two categories of water. Since water in the bigger pipe has more mass than that in the smaller pipe, it therefore has more kinematic force than that in the smaller pipe a feature that enables the water to counter the drag and therefore flow faster than the water in the smaller pipe. This explains the trend in housing and in constructions of cases that rely on gravitational force; the constructors often show preference to bigger pipes since they carry larger volumes of the liquids and therefore greater masses of the liquid thus enabling their faster speed and higher pressure.

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