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The percent error for this flow corresponds to 30.46%, while the error for the second flow was 33.088%. This percent error was drastically higher than the percent error associated with the velocity downstream of the sluice gate. The percent error of V2was 3.6% for the first flow and 2.9% for the second flow. Measuring the first flows velocity it was found to be 2.4221 m/s while calculating itstheoretical value to be 2.5135 m/s; for the second flow the measured velocity was 10 Lab manual
3.0496 m/s and the theoretical was 3.1415 m/s. The volumetric flow rate as well as the velocity of the two flows was recorded in Table #2 of the Appendix.The assumptions applied to Bernoulli’s equation as well as the ones applied to the continuity and momentum equations are not 100% valid and therefore introduce error into our associated calculations of the Velocity upstream and downstream of the sluice gate. As a result of the Bernoulli’s equation not taking heat and energy lostdue to friction into account the theoretical velocities are higher than the experimental velocities11. Bernoulli’s equation also implied an incompressible flow and from the analysis it can be seen that the flow is only incompressible when operating at supersonic speeds between the sluice gate and hydraulic jump12. As stated above, the measured velocity upstream of the sluice gate had a greater percent error in its calculations as a result of the V-notch equation not taking into consideration the velocity of the flow in the reservoir. The velocities found downstream of the sluice gate minimized the percent error as fewer assumptions were made and the ones that were applied were valid throughout the system.The total head loss in the system from the point upstream and downstream of the sluice gate can be represented by the mechanical energy content lost by the moving fluid13. Theoretically from the flow analysis the two points should contain the same amount of mechanical energy and therefore have zero head loss. From analyzing the data in table 1 of the appendix it can be shown that there is mechanical energy lost by passing under the sluice gate. This loss of mechanical energy can most likely be attributed to the frictional forces that were assumed to be zero. By moving under thesluice gate the fluid flow lost energy due to friction between the water and the waterchannel/gate14.The knowledge of control volume was applied to the hydraulic jump as well as the continuity and momentum equations in order to derive an expression, z3, for the theoretical water depth downstream of the hydraulic pump as a function of upstream depth, z2, and flow rate, Q15. The equation (17) was found by letting both 1-D flow forces equal one another and rearranging to find z3as a function of z2. The quadratic formula was then applied to solve for z3. The theoretical depth of the water downstream of the hydraulic jump was found to be 0.10655 m and measured 11 F.M. White, Fluid Mechanics, 7th Ed., McGraw-Hill, 2010, 257.