CIVI 381 Lab Report 3 and 4

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McGill University *

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381

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Mechanical Engineering

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Dec 6, 2023

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CIVI 381 Lab Report 3 & 4 Hydraulic Jump & Submerged Hydraulic jump Section: AK-X Due Date: May 31 st , 2023 Concordia University

Objective Two experiments are discussed in this report, both of which are related to the validation of the hydraulic jump theory. The formation of a hydraulic jump must be confirmed, a specific force diagram must be generated based on experimental measurements, a specific energy diagram must be generated based on experimental measurements, and the amount of energy lost during the jump must be calculated in order to validate the theory. Introduction When a supercritical flow (at cross section 2) quickly changes into a subcritical flow, it is known as the hydraulic jump phenomena. Here is a diagram that shows the various cross sections from the lab instructions. At cross section 3, the depth changes as a result, and the flow slows down. The continuity, energy, and momentum equations should be employed to analyse this occurrence; you can find all three of them here. Figure 1: Sections of Flow

Equipment & Procedure Materials: - Rectangular glass-walled flume with a downstream control - Pump for steady water supply - Sluice gate that creates supercritical flow - Tailgate to create a hydraulic jump - Depth gauges - Flow meter for measuring the discharge Procedure: Begin by utilising a machined block beneath the gate to set the sluice gate's opening to one inch. Afterward, note the flume's breadth. The lowest count of the depth gauges and their initial readings at each cross section are then recorded. Upstream valves should be adjusted to let water flow through the gate. Read the discharge from the flow metre after a while to acquire the supercritical flow. Calculate the flume's flow velocity and the Froude number. To create a hydraulic jump downstream from the sluice gate, pivot the tailboard in the downstream direction. Utilising the gauges, note the depths. Repeatedly record the depths after two more changes to the discharge. The same process must be followed for the experiment's second phase, except this time, a submerged hydraulic jump must be created by adjusting the tailboard. We will measure the beginning and end depths using three different discharge rates.

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Observations Table 1: Hydraulic Jump Measurements for Experiment 3 RUN 1 RUN 2 RUN 3 Y2i (cm) 4.7 4.7 4.7 Y2f (cm) 6.9 6.3 6.4 Y2 (m) 0.022 0.016 0.017 Y3i (m) 0 0 0 Y3f (m) 0.124 0.115 0.1019 Y3 (m) 0.124 0.115 0.1019 Q (m^3/s) 0.0118055 6 0.0108888 9 0.01 q (m^2/s) 0.0377174 3 0.0347887 8 0.0319488 8 v2 1.7144286 3 2.1742989 1.8793459 9 v3 0.3041728 2 0.3025111 5 0.3135317 2 Table 2: Run 1 Run 2 Run 3 Head Loss (  E) 0.13 0.22 0.16 Power Loss ( H p ) 15.08 23.86 16.18 Froude Number at Cross Section 2 ( Fr 2 ) 3.69 5.49 4.60 Froude Number at Cross Section 3 ( Fr 3 ) 0.28 0.28 0.1

Specific Energy Diagrams 0 2 4 6 8 10 12 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 E-y Diagram Run 1 E y (m) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 E-y Diagram Run 2 E y (m)

-1 1 3 5 7 9 11 13 15 0 0.05 0.1 0.15 0.2 0.25 E-y diagram Run 3 E y (m) Specific Force Diagrams 0 0 0 0.01 0.01 0.01 0.01 0.01 0 0.05 0.1 0.15 0.2 0.25 0.3 M-y Diagram Run 1 Fs y (m)

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0 0 0 0.01 0.01 0.01 0.01 0 0.05 0.1 0.15 0.2 0.25 0.3 M-y Diagram Run 2 Fs y (m) 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 M-y Diagram Run 3 Fs y (m) Run 1 Run 2 Run 3 Head loss 0.097 0.132 0.088 Difference 3.30 9.15 7.66 Strength 5.64 7.19 5.99 Lab 4 Observations

Run #1 Run #2 Run #3 (y2i) (cm) 0 0 0 (y2f) (cm) 2.54 2.54 2.54 (y2) (cm) 2.54 2.54 2.54 Record the gate opening cm 2.54 2.54 2.54 Initial reading of the submerged depth immediately downstream of the gate (yi) (cm) 4.7 4.7 5.0 (yf) (cm) 11.1 10.6 11.4 The submerged depth immediately downstream of the gate(y) (cm) 6.4 5.9 6.4 (y3i) (cm) 0 0 0 (y3f) (cm) 11.7 12.6 14.1 (y3) 11.7 12.6 14.1 Discharge (Q) (m^3/h) 35.1 40.2 45.4 Lab 4 results Ru n y 2 (m) y* (m) y 3 (m) v 3 (m/s) √ gy 3 Fr 3 y 3 y 2 1 − y 3 y 2 1 + 2 Fr 3 2 ( ¿ 1 − y 3 y 2 ) √ ¿ y** 1 0.025 4 0.06 4 0.117 0.0036 1.07 0.003 4 4.6 -3.6 0.9999 2 0.025 4 0.05 9 0.126 0.0045 1.11 0.004 4.96 -3.96 0.9999 3 0.025 4 0.06 4 0.140 9 0.0056 5 1.18 0.004 8 5.55 -4.54 0.999

Remarks and Conclusion Between cross-sections 2 and 3, where the flow condition changes from supercritical to subcritical, is where the hydraulic jump can be seen to occur. To demonstrate this behaviour, a SED and an SFD were also developed. The SED displays the head loss and flow conditions at the cross-sections. The graph's trend appears to show that there is more energy, as expected, with higher discharge rates. Two methods of calculating head loss were evaluated with differences in percentage ranging from 3.3 to 7.67%. The values of the difference are not far, which confirms that our values must’ve been within range with minimal mistakes

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Sample Calculations Lab #3 Discharge per unit weight of flume width, q (Run #1): q = Q / b q = ( 42.5 3600 ) 0.313 q = 0.0377 m 3 / s Specific Energy at cross section 1, E (Run #1): E 1 = E 2 E 2 = y 2 + q 2 2 gy 2 2 E 2 = 0.022 + 0.0377 2 2 ( 9.81 )( 0.022 2 ) E 2 = 0.172 m Head Loss Run 1 E 2 = y 2 + q 2 2 g y 2 2 = 0.022 + ( 42.5 ÷ 3600 ÷ 0.313 ) 2 2 × 9.81 × 0.022 2 = 0.150 m Power loss (H p ) (W): H P = ρgQ ∆ E = 1000 × 9.81 × 42.5 ÷ 3600 × 0.13 = 15.08 W Froude number at cross section 2 (F r2 ): Fr 2 = v 2 √ g y 2 = 45.2 ÷ 3600 ÷ 0.313 ÷ 0.022 √ 9.81 × 0.022 = 3.69 Froude number at cross section 3 (F r3 ): Fr 3 = v 3 √ g y 3 = 45.2 ÷ 3600 ÷ 0.313 ÷ 0.124 √ 9.81 × 0.124 = 0.28

Momentum M (m): M 2 = 0.5 y 2 2 + q 2 g y 2 = 0.5 × 0.022 2 + ( 45.2 ÷ 3600 ÷ 0.313 ) 2 9.81 × 0.022 = 0.00769 kgm / s Head loss (∆E) (m): ∆ E = ( y 3 − y 2 ) 3 4 y 2 y 3 = ( 0.124 − 0.022 ) 3 4 × 0.124 × 0.022 = 0.097 m