Specific energy, Hydraulic jump and Weirs

Experiment H3- Specific Energy, Hydraulic Jumps & Weirs

Experiment H3- Specific Energy, Hydraulic Jumps & Weirs

Objective:The purpose of this lab was to determine the relationship between specific energy and the upstream head for water flowing over a overshot crested weir, to study the properties of hydraulic jump and determine the flow patterns, and to study the relationship between upstream head and discharge for water flowing over a broad crested weir and to study the flow patterns.

Apparatus:The apparatus used in this lab consisted of a multi-purpose teaching flume, adjustable undershot weir and hook and point level gauge. Broad Crested Weir in flume Sharp Crested weir in flume Gauges

Theory:

The dynamics of hydraulic jump is governed by the flow continuity and the momentum equation. As we shall see, one of the major characteristic of a hydraulic jump is its large energy dissipation. Therefore, energy equation cannot be used at this point because the head loss is unknown (and not negligible). Using a control volume enclosing the jump as shown in Figure 1, the continuity equation is expressed as =11=22Where Q is the discharge, V represents the averaged velocity and h is the water depth. The subscript 1 and 2 represent flow information upstream and downstream of the hydraulic jump, respectively. The momentum equation which takes into account the hydrostatic forces and the momentum fluxes, but ignores the friction at the channel bottom and at the side walls, can be shown as1/2121/222= (21)in which is the fluid density and g is the gravitational acceleration. If we define a momentum function as=2/2+2/2Then, using equation (1) we can show that equation (2) suggest 1=2From equation (1) and (2), it can be shown that the upstream and downstream flow depths are related by Where Fr1 is the Froude number of the upstream flow and is defined as For a hydraulic jump, the upstream flow is supercritical and Fr1>1. On the other hand, the Froude number Fr2 of the downstream subcritical flow needs to satisfy It can be further applied to conservation of energy for this open channel flow problem as And show that the head loss hL for hydraulic jump is calculated as Procedure1. First of all it was ensured that fume was leveled. The undershot weir assembly was then clamped securely to the sides of the channel at mid-way along the flume with the sharp edge on the bottom of the gate.2. The level gauges were adjusted, one upstream of the weir and other downstream, to coincide with the bed of the flume and the datum readings were recorded.3. The knob on top of weir was adjusted to position the sharp edge of the weir 0.010 m above the flume bed.4. The flow control valve was gradually opened and water was allowed to flow in the channel until y0 measured 0.2 m. With y0 at this height, Q was measured and recorded using direct reading flow meter. Y1 was also measured and recorded using the downstream level gauge.5. The weir was raised in increments of 0.01 m, allowing the upstream and downstream levels to stabilize. Y0 and y1 were measured and recorded.6. The flow rate was increased slightly. Q was measured and recorded. Above measurements were repeated by gradually raising the weir.Hydraulic Jump7. The undershot weir was repositioned so that assembly was securely clamped to the sides of the channel.8. The knob on top of the weir was adjusted to position the sharp edge of the weir 0.020 m above the bed of the flume. 9. The flow control valve was gradually opened. A hydraulic jump was produced decaying towards the discharge end of the flume. 10. Values of y1, y3, yg and Q were measure and recorded. The procedure was repeated for four other flow rates Q and heights of the gate, yg.Broad Crested Weir11. The broad crested weir was installed in the flume with the rounded corner upstream. 12. The level gauges were adjusted to coincide with the bed of the flume and the datum readings were recorded. 13. The height of the weir was measured above the bed P.14. The flow of water was adjusted into the flume to obtain. For each trial the flowrate Q, the upstream depth of flow y0 and the depth of flow over the weir yc were measured. Specific energy, Hydraulic jump and Weirs[Type the date]

Specific energy, Hydraulic jump and Weirs

15. Results and CalculationThe following of the calculations and results were obtained after the experiment;

Table-1 Specific Energy CalculationsQ =0.002

Emin = 0.0747 m

y0 (m)y1 (m)E0 (m)E1 (m)

0.1420.0220.1450.149

0.1230.0240.1270.131

0.1140.0250.1190.123

0.1010.0270.1070.111

Q =0.0018

Emin = 0.068 m

y0 (m)y1 (m)E0 (m)E1 (m)

0.1520.0210.1550.160

0.1340.0230.1370.139

0.1220.0250.1260.123

0.1100.0260.1150.117

Q =0.0016

Emin = 0.063

y0 (m)y1 (m)E0 (m)E1 (m)

0.1060.0220.1100.117

0.0980.0230.1030.110

0.0850.0260.0910.094

0.0790.0270.0860.090

Specific energy, E0 and E1 (x-axis) vs depth of flow, y0 and y1 for each flow rateFor Q=0.002

For Q=0.0018

For Q=0.0016

Table-2 Hydraulic Jump Calculationsyg (m)y1 (m)y3 (m)Q (m3/s)H (m)V1(m/s)V1^2/gy1y3/y1

0.0300.0380.0590.0020.0011.5166.1631.553

0.0330.0350.0610.0020.0021.6467.8881.743

0.0350.0340.0630.0020.0031.6948.6051.853

0.0380.0310.0690.0020.0061.85811.3522.226

0.0280.0380.0580.0020.0011.3634.9851.526

0.0300.0360.0590.0020.0011.4395.8631.639

0.0320.0350.0610.0020.0021.4806.3791.743

0.0340.0330.0640.0020.0041.5707.6111.939

0.0300.0300.0580.0020.0031.5378.0241.933

0.0320.0280.0590.0020.0051.6469.8692.107

0.0350.0270.0630.0020.0071.70711.0062.333

0.0370.0270.0630.0020.0071.70711.0062.333

Table-3- Broad Crested Weir clculationsWeir Type: Broad Crested Weir

Breadth of Weir b = 0.0347 m Height of Weir P =0.0098 m

y0 (m)yc (m)Q (m3/s)H3/2Cdhu3/2Cv

0.1710.1440.00180.0740.4130.0651.138

0.1660.1410.00160.0700.3860.0621.135

0.1640.1390.00150.0690.3700.0611.133

0.1610.1370.00140.0670.3560.0591.132

Graphs: The critical depth under various flow rates;At Q= 0.002Emin = 0.074 m

Graph-2At Q=0.0018Emin = 0.068 m

Graph-3At Q=0.0016Emin = 0.063

Loss of energy through a hydraulic jumpGraph-4Specific Energy Curves for each value of Q

Graph-5 y3/y1 (x-axis) vs H

Broad Crested WeirGraph-6Total Head (x-axis) vs. Flow rate

Graph-7 Log H (x-axis) vs Log Q

Graph-8 Total Head (x-axis) vs. Cd

Discussion and ConclusionThe experiment determined the relationship between discharge and head for water flowing over overshot weir, properties of hydraulic jump and discharge-relationship for broad crested weir.In the overshot weir experiment specific energy curves were plotted. The shapes of curves are similar to the theoretical curve. It was observed that with decreasing discharge critical depth also decreased due to which minimum energy also decreased. The calculated values of minimum energy are same as the values obtained from curves.In the hydraulic jump experiment difference in head was measured. Graphs between y3/y1 versus H and V12/gy1 were plotted. Both graphs show that with increase in y3/y1, H and V12/gy1 increases.In the broad crested weir experiment, Cd and Cv were measured. When the flow of water was parallel to the weir, that point showed that critical depth has been achieved. Coefficient of discharge changed with the flow rate. It increased with the increasing flow rate. As water passed through the weir the depth of flow deceased and the profile of water was observed to change. Broad crested weirs are robust structures that are generally constructed from reinforced concrete and which usually span the full width of the channel. They are used to measure the discharge of rivers, and are much more suited for this purpose than the relatively flimsy sharp crested weirs. Additionally, by virtue of being a critical depth meter, the broad crested weir has the advantage that it operates effectively with higher downstream water levels than a sharp crested weir.Length of weir has no effect on the discharge coefficient. It only depends on the breadth and height of the weir. There is a very little increase in the values of Cv with increasing flow rate. The common values of discharge coefficient of broad crested weir varies but it is usually 1.6 m. The calculated values are very less than the theoretical values.The experimental results are good but the values of discharge coefficient are less than the theoretical values. Possible sources of error may be in handling the apparatus. There may be error in noting the reading and in predicting the accurate point of critical depth.

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