Introduction
The experiment was conducted to establish the association between head loss as a result of fluid friction and the flow rate of water. Turbulent and laminar flow within the pipe were also investigated. Fluid Friction Equipment containing three bore pipes was used to take the data of head loss at dissimilar velocities. Different readings on volume, time, flow rate, pipe diameter, and velocity and head loss of both mercury and water were collected. The data collected were used to investigate the association between head loss due to friction and the flow rate of water through bore pipes. An estimate of the coefficient of friction will be obtained using the head loss or pressure drop and the velocity of the fluid through the pipe.
Literature Review
Fluid flow is a significant component of numerous processes including mixing of materials, transporting of fluids from one point to another and chemical reactions. The flow of fluid through a pipe can be categorised into two groups; turbulent and laminar flow. Laminar flow is a type of flow exhibited by fluids at low velocity. The movement of fluid in laminar flow is characterised by slow motion of fluid in layers within the pipe devoid of much mixing among the fluid layers. In most cases, laminar flow occurs when the fluid is viscous or when the fluid is travelling at low velocity (White and Isla 35). On the other hand, turbulent flow occurs at high velocity and entails a lot of mixing among the fluid layers. Re is utilized to quantify and characterise both turbulent and laminar flows.
Nr=VDρŋ
Nr=VDv
Where Nr is the Re, V is the flow rate of the fluid (velocity), D represents the pipe’s diameter, ρ represents water density, n is the dynamic viscosity and v is the kinematic viscosity. It is imperative no note that Re is inversely proportional to viscosity and directly proportional to the fluid’s velocity. To determine, characterise and quantize the type of flow in a fluid, it is imperative to establish the Re using the fluid’s velocity, density and the pipe’s diameter. The obtained Re is measured against the preset standard used to establish the type of flow exhibited by a fluid. In case the quantity of the Re obtained is less than 2000, then the fluid exhibits a laminar flow.
On the other hand, in case the Re obtained by the fluid is more than 4000, then the fluid exhibits a turbulent flow. There is a transition region or critical region between a turbulent and laminar flow. Re for a fluid flow that exists between 2000 and 4000 is regarded as the critical or the transition region (White and Isla 35). At this region, the flow of fluid prepares to change from laminar flow to turbulent flow or from turbulent flow to laminar flow. In most cases, more viscous fluids tend to poses lower Re or laminar flow.
The pressure difference due to friction for a pipe is obtained through the following formula;
h= 2fLu2gd
Where L the pipe’s length between tapings, u is the average velocity, d represents the pipe’s internal diameter, g is the force due to gravity and f represents friction coefficient of the pipe.
The average fluid’s velocity is attained through;
u=4Qπd2
Where Q is the volumetric flow rate
The experimental value of the coefficient of friction is obtained when the head loss is measured experimentally.
f=hgd2Lu2
Methodology
The experiment was accomplished through the use of the following materials, apparatus and equipment; Fluid Flow Apparatus, water, Internal Vernier callipers and a stop watch.
Experimental procedure
A sequence of steps was employed so as to gather a collection of data of pressure drop at different velocities through the test pipes. The network of test pipes was primed with water. The appropriated valves were opened and closed so as to attain flow of water though the needed test pipe. The volumetric reservoir in conjunction with the flow control valve V6 was used to determine the flow rates. Valve V6 was closed and measuring cylinder together with flow control valve V5 was used to measure small velocities. The pressure drop amid the tappings was measured using mercury manometer. The readings on the test pipes 1, 2 and 3 were obtained. The interior diameter of the test pipe was measured using a Vernier calliper.
Results and Discussion
The curve of head loss, h against velocity, u
The graph of log h against log u
Gradient of the curve to determine the value of n;
n=change in log h/change in log u= (1.505-1.097)/(0.475-0.209)
n = 0.408/ 0.266
n= 1.534
It is significant to indicate that laminar flow occurs at low velocity and exhibits a different head loss and velocity association from turbulent flow. While the association between head loss and velocity remains directly proportional, a difference between the two kinds of flow exists in the flow rate of the fluid. For a laminar flow, the pressure drop due to fiction is directly proportional to the velocity of the fluid flow. On the other hand, turbulent flow exhibits a totally different relationship between the head loss and the flow rate of the fluid. It is imperative to indicate that turbulent flow occurs at high velocities. As a consequence, the pressure drop exhibited in turbulent flow is directly proportional to the square of the flow rate.
For laminar flow;
head loss, h∝velocity, u
For turbulent flow;
head loss, h∝velocity, u2
A curve of head loss against the fluid flow velocity indicates the relationship that exists between the head loss and the fluid’s flow rate at different stages of the flow. At the laminar flow stage, the head loss is directly proportional to the fluid’s flow rate. A region exists between the laminar flow and the turbulent flow where the type of flow cannot be categorised as either laminar or turbulent flow (White and Isla 47). The region is known as a transition or critical region. At this region, there is no definite association between head loss and velocity of the fluid flow.
Conclusion
The flow of fluid through a pipe exhibit head loss due to various factors including the flow rate of the fluid. The difference in pressure in the flow of the fluid can be equated to the velocity of the fluid's flow. Other factors that affect the head loss of the fluid include the pipe’s diameter, the fluid’s viscosity as well s the fluids flow rate.
Works Cited
White, Frank and Isla Corfield. Viscous fluid flow. Vol. 3. New York: McGraw-Hill, 2006.
