Fluid Flow Measurements - Lab Report Example

Flow Measurement Lab Report Name Institution of Affiliation Date Introduction Incompressible fluids such as water are of major interest to engineers. This is because they are utilized in all manner of applications and understanding their behavior is a necessary prerequisite. One of the main characteristics of these fluids is flow patterns. This is described in terms of discharge, the rate at which a fluid such as water flows through a section. The discharge is affected by multiple factors and these include the viscosity of the fluid, the velocity of flow, the slope of the channel, and the geometrical shape of the conduit. It is therefore necessary to determine this rate for any specific fluid under the given conditions so as to ensure that any applications that rely on it are done accurately. There are various flow rate measurement methods, one of the most common being the use of a Venturi meter, an orifice plate meter and a rotameter. These devices principally work by monitoring the quantity of fluid that passes through them over a given period of time. Dividing the volume by the time gives the discharge and hence the flow rate. There are multiple applications that rely on deducing the flow rate and include designing the size of a dam; design specifications for drainage urban drainage systems; estimating the pipe and canal sizes for an irrigation system, and calculating the quantity of water delivered to a pump or turbine. The main objectives of performing this experiment were to: 1. Determine the rate of discharge through the apparatus 2. Estimate the head losses associated with the passage of fluid through the measurement devices 3. Determine the mass flow rate for the fluid. Apparatus and Set Up The following apparatus were used for this experiment: 1. Rotameter 2. Venturi meter 3. Orifice plate meter The figures below illustrate how the devices were set up during the experiment: Fig 1: flow measurement apparatus Fig 2: Explanatory diagram of the flow measurement apparatus Experimental Procedure 1. The devices were initially prepared in three steps: Firstly, the hoses from the hydraulic bench were connected to devices and secured appropriately. Next, the air purge was sealed and the flow measurement apparatus filled with water. Finally, blockages were checked and removed from the tube ferrules and the top manifold 2. The control valve was kept fully open. The apparatus valve was opened until the point where the reading on the rotameter was about 10 mm. One a steady flow was maintained, it was measured with the flow meter. These readings and that of the other devices were then recorded 3. Step 2 was repeated for a continuous number of 10-mm rotameter readings until where the maximum value of pressure could be recorded from the manometer. Results and Calculations In order to calculate the flow there are certain parameters that must be calculate. The main one among these is the change in the inlet kinetic head. This is because as the water flows through the apparatus, there is a reduction in the head due to friction and fittings. Therefore, the results obtained are first used in the calculation of this difference at five points: (i) At the venturi ∆Hv = (ii) At the orifice meter ∆Ho = (iii) At the Elbow bend ∆He = (iv) At the Diffuser ∆Hd = [) + (∆Hv - )]/ ∆HV (v) At the rotameter ∆Hr = (-10 + ( HH+ HI))/ ( The water was assumed to have flowed over a length L of one meter and the inlet diameter D taken as that of the between manomter tubings A and B with water density ᵨ. Therefore, the mass flow rate could be obtained by: M = (πD2/4)*L)* ᵨ Kg/s The collected and calculated data were tabulated as shown below: Table 1: Experimental Results The data was used in generating curves with the head loss as a function of the mass flow rate for the each of the given meters: These are shown in the figures below: Fig 3: ∆H against M at the (a) Venturi meter (b) Diffuser Fig 3: ∆H against M at the (a) Orifice (b) Rotameter Fig 4: ∆H against M at the elbow bend Discussion From the curves drawn using the data, it was observed that they differ from one another depending on the fitting through which the water was flowing. This can be attributed to the fact that they had geometric differences in terms of size and alignment. At the venturi meter, the head loss rapidly drops before rising at an equally fast rate and subsequently reducing in an oscillatory manner as the quantity of mass flow rate increases. This is because as the water enters the venturi, the constriction causes a sharp increase in the velocity as the head decreases. Thereafter, the diameter of the venturi increases and so does the associated change in head. The changes thereafter occur at a slower rate since the diameter does not vary as sharply as before but slowly increases before becoming uniform (Falkovich, 2011). In the diffuser, the curve generally has a positive gradient which indicates that the change in head was continuously increasing. However, there were slight drops along the curve and hence it assumes a meandering pattern. When an incompressible fluid like water is passed through a diffusor, it moves over channels of varying diameters. Since it cannot be compressed, the flow does not smoothen and hence there is a continuous change in the head. This is observed by peaks when the channel diameter increases and the crest when it decreases. The graph showing the passage of the fluid passing through an orifice is a curve with a sharp gradient crossing close to the origin. If a line of best fit is plotted, it reveals that the curve has approximately a constant gradient. This shows that the rate at which the head changes as the water flows through an orifice is nearly constant and continuously rises. It is because the shape of the orifice does not change from one point to another and hence the fluid flows smoothly. However, frictional losses and minor obstructions that the fluid may come across lead to a decrease in the change of head. The curve of the flow through the rotameter is at best described as sinusoidal. This is due to the fact that the curve is observed to smoothly move from peaks before reaching crests and then moving up again. A rotameter is a variable area meter and hence as the fluid passes through it, the area of the pipe changes. When the area is decreased, the change in head increases and vice versa. Since this is a continuous process and the meter rotates at a constant rate, the curve assumes a sinusoidal shape with a general upward trend. It can therefore be stated that the change in head increases as the fluid moves further within the device. Finally, the water was also passed through an elbow joint. Pipe fittings such as this one cause an impediment to the flow of water and hence resulting in changes in the head. Based on the curve, it is observed that the change is positive at the onset before falling, shooting up again, and finally leveling off. This is because as the water approaches the curve, there is a slight rise in the head before it rapidly decreases as once it reaches and as it passes through the bend. The head then increases once the water has in its entirety passed through the bend. This results in a positive change before it levels of as it enters the rest of the piping system. Errors in the Lab In any experiment, there is bound to be an occurrence of errors which interfere with the quality of the data collected and used. That is the reason why many experimental values differ from the theoretical ones. In this experiment, there are some errors which might have occurred. These include: 1. Presence of air in the manometer Even though the apparatus were allowed to fill with water, there may have been sections which contained air. These might not have been noted and hence the air was not expelled. As a result, the rise in the apparatus may not have reflected the true picture of the experiment. The recorded values were therefore possibly inaccurate. 2. Blockage of Water Blockage of water might occur in the ferrules or top manifolds due to the presence of foreign particles. This therefore suppresses the flow of water and not only varies the quantity discharged but also the flow velocity. As a result, the wrong readings might be taken as the rise in the manometer may be interfered with by such blockages. 3. Reading and Computational Errors When making the readings, the incorrect values might have been observed and hence recorded due to errors in judgment or parallax. Furthermore, errors might have been introduced in the data set when making computations due to rounding up and truncations. Conclusion Based on the results, the following conclusions can be made: 1. The kinetic head of an incompressible fluid changes with changes in the mass flow rate 2. The type and degree of change in the kinetic head is dependent on the type of pipe fitting the fluid passes through 3. The value of the observed changes might be different from theoretical ones due to experimental errors Reference Falkovich, G. (2011). Fluid Mechanics, a short course for physicists. Cambridge University Read More

Step 2 was repeated for a continuous number of 10-mm rotameter readings until where the maximum value of pressure could be recorded from the manometer. Results and Calculations In order to calculate the flow there are certain parameters that must be calculate. The main one among these is the change in the inlet kinetic head. This is because as the water flows through the apparatus, there is a reduction in the head due to friction and fittings. Therefore, the results obtained are first used in the calculation of this difference at five points: (i) At the venturi ∆Hv = (ii) At the orifice meter ∆Ho = (iii) At the Elbow bend ∆He = (iv) At the Diffuser ∆Hd = [) + (∆Hv - )]/ ∆HV (v) At the rotameter ∆Hr = (-10 + ( HH+ HI))/ ( The water was assumed to have flowed over a length L of one meter and the inlet diameter D taken as that of the between manomter tubings A and B with water density ᵨ.

Therefore, the mass flow rate could be obtained by: M = (πD2/4)*L)* ᵨ Kg/s The collected and calculated data were tabulated as shown below: Table 1: Experimental Results The data was used in generating curves with the head loss as a function of the mass flow rate for the each of the given meters: These are shown in the figures below: Fig 3: ∆H against M at the (a) Venturi meter (b) Diffuser Fig 3: ∆H against M at the (a) Orifice (b) Rotameter Fig 4: ∆H against M at the elbow bend Discussion From the curves drawn using the data, it was observed that they differ from one another depending on the fitting through which the water was flowing.

This can be attributed to the fact that they had geometric differences in terms of size and alignment. At the venturi meter, the head loss rapidly drops before rising at an equally fast rate and subsequently reducing in an oscillatory manner as the quantity of mass flow rate increases. This is because as the water enters the venturi, the constriction causes a sharp increase in the velocity as the head decreases. Thereafter, the diameter of the venturi increases and so does the associated change in head.

The changes thereafter occur at a slower rate since the diameter does not vary as sharply as before but slowly increases before becoming uniform (Falkovich, 2011). In the diffuser, the curve generally has a positive gradient which indicates that the change in head was continuously increasing. However, there were slight drops along the curve and hence it assumes a meandering pattern. When an incompressible fluid like water is passed through a diffusor, it moves over channels of varying diameters.

Since it cannot be compressed, the flow does not smoothen and hence there is a continuous change in the head. This is observed by peaks when the channel diameter increases and the crest when it decreases. The graph showing the passage of the fluid passing through an orifice is a curve with a sharp gradient crossing close to the origin. If a line of best fit is plotted, it reveals that the curve has approximately a constant gradient. This shows that the rate at which the head changes as the water flows through an orifice is nearly constant and continuously rises.

It is because the shape of the orifice does not change from one point to another and hence the fluid flows smoothly. However, frictional losses and minor obstructions that the fluid may come across lead to a decrease in the change of head. The curve of the flow through the rotameter is at best described as sinusoidal. This is due to the fact that the curve is observed to smoothly move from peaks before reaching crests and then moving up again. A rotameter is a variable area meter and hence as the fluid passes through it, the area of the pipe changes.

When the area is decreased, the change in head increases and vice versa. Since this is a continuous process and the meter rotates at a constant rate, the curve assumes a sinusoidal shape with a general upward trend. It can therefore be stated that the change in head increases as the fluid moves further within the device.

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