Learning Objectives Observe the hydraulic jump downstream of hydraulic structures such as a sluice gate in an open channel flume ● E4: HYDRAULIC JUMP IN FLUME Compare observed and theoretical ratios of upstream and downstream depths. Quantify the energy lost due to a hydraulic jump. Theory of the Experiment In engineering practice, the hydraulic jump frequently appears downstream from overflow ructures (spillways) or underflow structures sluice gates) where velocities are high. The hydraulic jump is a rapid transition from supercritical flow to subcritical flow. It is formed when liquid at high velocity discharges into a zone of lower velocity, creating a rather abrupt rise in the liquid surface (a standing wave) accompanied by violent turbulence, eddying, air entrainment, and surface undulations The transition is generally a turbulent process with a significant energy loss(AE), that cannot be neglected. A hydraulic jump is commonly used to dissipate energy, and reduce the downstream velocity. Figure 1 shows the variables included in a hydraulic jump. EGL JE E₁ Flow yg A flow is supercritical when: √²/2g VI Jump F₁ r Figure 1: Hydraulic Jump Illustration = F₁ V = > 1 ΔΕ 1 Where, F, is the Froude number, V is the fluid velocity, g is the gravitational constant, and y is fluid depth. For a channel of rectangular cross-section and constant width: 9 y √gy E₂ I V2/2g Y2 Where q=Q/b, the flow rate per unit width of the channel. In supercritical flow, disturbances travel downstream, and upstream water levels are unaffected by downstream control. Supercritical flows are characterized by high velocity and small flow depth and are also known as shooting flows. A flow is subcritical when: Fr = V <1 In subcritical flow, disturbances travel upstream as upstream water levels are affected by downstream control. Subcritical flows are characterized by low velocity and large flow depth and are also known as tranquil flows. In a hydraulic jump, supercritical flow changes to subcritical flow over a short horizontal distance. where, E₁ = upstream energy, (m) E2= downstream energy, (m) AE = energy loss, (m) In horizontal rectangular channels, the relationship between the downstream and upstream depths of a hydraulic jump is given by the following equation: 22 - - (√1+8F² -1) = Y₁ where, y₁ = upstream depth of jump (m) y2= downstream depth of jump (m) F₁ = Froude number for upstream flow In addition, the critical depth of a rectangular channel can be calculated as follows: Y₁ = Where, q is the flowrate per unit width (Q/b) (m² /s). This critical depth can be used to characterize whether a flow is subcritical (y>yc) or supercritical (y<yc). The energy loss during the jump can be evaluated as follows: g AE = E₁-E₂ (y₁ - y₁)² 4y112 According to the U.S. Bureau Reclamation (USBR), a hydraulic jump can be classified in undular, weak, oscillating, steady, and strong jump. Table 1 shows the classification. Table 1: Characteristics of Hydraulic Jump (USBR 1955) [1] F₁ Energy dissipation < 5% 1.0 1.7 1.7-2.5 5 - 15% 2.5-4.5 15 - 45% 45-70% 70 - 85% Name Undular jump Weak jump Oscillating jump Steady jump Strong jump 4.5 9.0 > 9.0 Experimental Procedures A sluice gate is installed in the flume used to generate the hydraulic jump. The flume should be leveled. The sluice gate will create a supercritical flow immediately after the gate, followed by a hydraulic jump, and then a subcritical flow downstream of the hydraulic jump. Clamp the sluice gate assembly securely to the sides the channels close to the upstream end of the flume with sharp edge on the bottom of the gate facing upstream. For accurate results, the gaps between the gate and channel should be sealed on the upstream side using Plasticine. One level gauge is located upstream of the hydraulic jump to measure the supercritical depth, yı, and the other downstream of the hydraulic jump to measure the subcritical depth, y2. The gauges are zeroed with the bed of the channel and have to be moved depending on the location of the hydraulic jump. Measure the accurate flowrate, the upstream depth and the downstream depth. Steps 1. Adjust the knob on top to position the sharp edge of the gate 0.015m above the bed of the flume. Place one stop log at the discharge end of the flume. 2. Gradually open the flow control valve and adjust the flow until an undular jump is created with small rippled decaying towards the discharge end of the flume. Observe and sketch flow pattern. 3. Increase the height of water upstream of the gate by increasing the flowrate and increase the height of the stop logs to create a hydraulic jump in the center of the working section. Observe and sketch the flow pattern. 4. Move one level gauge to the region of rapid flow just upstream of the jump. Move the second level gauge to the region of tranquil flow just after the jump. Measure and record the values of y¹, №², yg and Q. 5. For each sluice gate opening, collect data for 4 different flow rates. 6. Repeat steps 1 through 5 for a sluice gate opening of 0.020m. Data Analysis and Discussions 1. Calculate the Froude numbers for the upstream depth y₁ (F₁) and downstream depth y2 (F₂) a. Do you see a transition from supercritical depth to subcritical depth? b. Classify the type of jump based on the upstream Froude number. 2. Calculate the critical depth (ye) for all flow rates. a. Check whether your subcritical depths are greater than critical depths and your supercritical depths are less than your critical depths. 3. Calculate the theoretical downstream depth, y using the measured upstream depth (y₁). Plot y₂ /yl vs y₂/y₁ on graph. Do the measured and theoretical downstream depths match? 4. Calculate the loss of energy (AE). For each gate opening, plot the energy losses (4) in the jump as a function of flow rate (Q). How does energy loss change with flow rate? 5. Suggest an application where the loss of energy in hydraulic jump would be desirable. How is the energy dissipated? Data Sheet Breadth of gate, b Gate Trial opening, Yg (m) 1 2 3 4 5 6 7 8 (m) Table 2: Hydraulic Jump Experiment Data and Results Experimental Data Upstream Downstream depth, depth, yı (m) y2 (m) Volume of water collected in tank, V (L) Time to collect volume of water, t (s) Q (m³/s) Calculated Data F1 F2 ΔΕ ye | y (m) | (m) | (m)/nExperimental Procedures A sluice gate is installed in the flume used to generate the hydraulic jump. The flume should be leveled. The sluice gate will create a supercritical flow immediately after the gate, followed by a hydraulic jump, and then a subcritical flow downstream of the hydraulic jump. Clamp the sluice gate assembly securely to the sides of the channels close to the upstream end of the flume with sharp edge on the bottom of the gate facing upstream. For accurate results, the gaps between the gate and channel should be sealed on the upstream side using Plasticine. One level gauge is located upstream of the hydraulic jump to measure the supercritical depth, yı, and the other downstream of the hydraulic jump to measure the subcritical depth, y2. The gauges are zeroed with the bed of the channel and have to be moved depending on the location of the hydraulic jump. Measure the accurate flowrate, the upstream depth and the downstream depth./nSteps 1. Adjust the knob on top to position the sharp edge of the gate 0.015m above the bed of the flume. Place one stop log at the discharge end of the flume. 2. Gradually open the flow control valve and adjust the flow until an undular jump is created with small rippled decaying towards the discharge end of the flume. Observe and sketch flow pattern. 3. Increase the height of water upstream of the gate by increasing the flowrate and increase the height of the stop logs to create a hydraulic jump in the center of the working section. Observe and sketch the flow pattern. 4. Move one level gauge to the region of rapid flow just upstream of the jump. Move the second level gauge to the region of tranquil flow just after the jump. Measure and record the values of y₁, y₁, yg and Q. 5. For each sluice gate opening, collect data for 4 different flow rates. 6. Repeat steps 1 through 5 for a sluice gate opening of 0.020m./nData Analysis and Discussions 1. Calculate the Froude numbers for the upstream depth y₁ (F₁) and downstream depth y2 (F2) a. Do you see a transition from supercritical depth to subcritical depth? b. Classify the type of jump based on the upstream Froude number. 2. Calculate the critical depth (yc) for all flow rates. a. Check whether your subcritical depths are greater than critical depths and your supercritical depths are less than your critical depths. 3. Calculate the theoretical downstream depth, y2 using the measured upstream depth (y₁). Plot y₂ /y1 vs y₂/y₁ on graph. Do the measured and theoretical downstream depths match? 4. Calculate the loss of energy (AE). For each gate opening, plot the energy losses (AE) in the jump as a function of flow rate (Q). How does energy loss change with flow rate? 5. Suggest an application where the loss of energy in hydraulic jump would be desirable. How is the energy dissipated?

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