Experiment (5): Flow through small orifices

Transcription

1 Experiment (5): Flow through small orifices Introduction: An Orifice is an opening in the side or base of tank or reservoir through which fluid is discharge in the form of a jet. The discharge will depend up on the head of the fluid (H) above the level of the orifice. The term small orifice means that the diameter of the orifice is small compared with the head producing flow. The analysis of the quantity of water which can be discharged through an orifice is arrived at in a simple, straightforward manner by the application of Bernoulli's equation. However, experimental tests typically produce a result which is only some 65% of the solution indicated by the simple analysis. The study of water flow through an orifice is therefore a classic topic to illustrate the need for a semi-empirical approach which is so often required in Mechanics of Fluids. Exercise A: Flow through a small orifice Purpose: To investigate the discharge characteristics of circular orifices subjected to a constant head. Apparatus: 1. Constant head inlet tank (Figure 1). 2. Circular orifices with different diameters. 3. Hydraulic bench. 1

2 Figure 1: Constant head inlet tank with circular orifice Equipment set up: Set up the apparatus on top of the hydraulics bench with the left hand support feet of the impact of jet apparatus located on the two left hand locating pegs of the hydraulics bench so that the apparatus straddles the weir channel. Connect the feed tube from the hydraulics bench to the boss on the rear of the base of the impact of jet apparatus. Fit the 5mm nozzle and the normal flat target. 1. If the hook gauge and scale are to be used to measure the trajectory of horizontal jets then place the two positioning rails on the worktop of the hydraulics bench engaging them onto the locating pegs. Ensure that the engraved rail is placed closest to the front of the hydraulics bench with the engraved side uppermost. 2. Position the constant head inlet tank onto the worktop of the hydraulics bench (over the hook gauge positioning rails, if fitted) at the left hand side engaging two of the feet of the inlet tank onto the locating pegs. If the orifice is to be fitted into the side of the inlet tank then it should be moved to the left so that the right hand support feet engage with the locating pegs. 3. Remove the hexagonal (37mm across flats) bush and adaptor from the side of the inlet tank. Fit the required orifice into the screwed hole in the side and plug the unusued hole using the blanking plug provided. 2

3 4. Connect the hydraulics bench flexible delivery tube to the connection provided on the rear of the inlet tank base. Insert the flexible overflow take off pipe, which is connected to the boss on the front of the inlet tank, into the overflow pipe of the volumetric measuring tank. 5. Remove or refit the overflow extention tube (screwed) in the inlet head tank to obtain a nominal head of 250mm or 500mm above the side orifice. A. Setting the overflow: Switch on the pump and control the flow rate by either adjusting the hydraulics bench delivery valve or by adjusting the pump speed. The flow should be adjusted carefully to produce a small but constant overflow and then fine adjusted to give 250 or 500mm head as required. B. Flow measurement: The discharge from the orifice may be measured using the volumetric measuring tank and taking the time required to collect a quantity of water. The quantity should be chosen so that the time to collect the quantity is at least 120 seconds to obtain a sufficiently accurate result. C. Measurement of jet trajectory: Use the hook gauge to measure the trajectory of the jet. D. Measurement of head: The scale attached to the side of the inlet tank has its zero level with the centre line of the side outlet boss. Theory: Consider a small orifice in the side of a vessel with the head of water above the orifice kept constant. Figure 2: Discharge through an orifice Applying Bernoulli's theorem between the surface of the water 1 and the orifice O yields 3

4 However = atmospheric pressure hence substituting these into Bernoulli's equation gives In other words, the theoretical velocity of the water passing through the orifice is given by and hence the quantity of water being discharged through the orifice is given by However in practice the discharge is always less than this theoretical amount due to the viscosity of the fluid, to surface tension and due to resistance of the air. The disparity between the theoretical discharge velocity and the actual discharge velocity is allowed for by introducing a factor known as the coefficien of velocity so that If the discharge from a sharp edged orifice is examined closely it will be observed that the minimum diameter of the jet of water discharging from the orifice is smaller than the orifice diameter. The plane at which this occurs is known as the vena contracta, which is the plane where stream lines first become parallel. Applying the discharge equation at the vena contracta which can be written as Where:. or more simply as Where:. Typical values of Cd range from 0 6 to 0 65, i.e. the actual flow through a sharp edged orifice is approximately 60% of the theoretical value. The value of the coefficient of discharge may be 4

5 determined by measuring the quantity of water discharged over a period of time whilst the head is maintained at a constant level. Procedures: 1. Fit the 5mm diameter orifice into the side of the inlet head tank. Remove the overflow extension pipe. Start the pump and set up an inlet head of 25cm. Measure the flow rate using the volumetric measuring tank. 2. Replace the overflow extension pipe and set up an inlet head of 50cm. Measure the flow rate. 3. Repeat the procedure using the 8mm orifice. Results: 1. Record the results on a copy of the result sheet for discharge characteristics. 2. For each result calculate the flowrate 3. Plot a graph of square root of the head against the flow rate for each orifice diameter, the results should lie on a straight line passing through the origin to confirm that: Measure the slope of each graph and calculate the coefficient of discharge for each orifice from D (mm) 5 8 H (cm) (m) V (L) T (sec) (m 3 /s) 5

6 Exercise B: Trajectory of horizontal jet Purpose: To investigate the trajectory of a horizontal jet issuing from an orifice and hence determine the coefficient of velocity for the orifice. Apparatus: 1. Constant head inlet tank (Figure 1). 2. Circular orifices with different diameters. 3. Hook gauge and scale. 4. Hydraulic bench. Theory: Consider the trajectory of a jet formed by the discharge of water through an orifice mounted in the side of a tank. The jet will be subjected to a downward acceleration of g due to gravity. Figure 3: Trajectory of horizontal jet Taking the origin of co-ordinates at the vena-contracta and applying the laws of motion in the horizontal and vertical planes then ignoring any effect of air resistance on the jet. In the horizontal direction In the vertical direction Solving simultaneously by eliminating t 6

7 Procedures: 1. Fit the 5mm diameter orifice into the side of the inlet head tank. Remove the overflow extension pipe. Start the pump and set up an inlet head of 25cm. 2. Measure the trajectory of the jet using the hook gauge. Record the horizontal and vertical distances. 3. Replace the overflow extension tube and establish an inlet head of 500mm. Measure the trajectory of the jet 4. Repeat the experiment using the 8mm diameter orifice. Results: 1. Draw a graph of y against x to represent the trajectory. 2. Draw a graph of against x and draw the best straight line through the points to represent the results. Measure the slope of the line and hence calculate the coefficient of velocity from: 7

8 D (mm) 5 8 H (cm) x (cm) Vertical distance below orifice center line y (cm) Slope of graph 8