E4: HYDRAULIC JUMP IN FLUME Learning Objectives ● Observe the hydraulic jump downstream of hydraulic structures such as a sluice gate in an open channel flume ● Compare observed and theoretical ratios of upstream and downstream depths. ● Quantify the energy lost due to a hydraulic jump.

Question 1 A long culvert has the cross-section of an equilateral triangle with side 0.7 m. The surfaces of the culvert have a Manning's roughness n = 0.012 m-¹/³s and the streamwise slope is 0.01. The culvert carries a flow of 0.35 m³ s. Assuming that the culvert does not run full, find the normal depth (measured from the lowest point) and the Froude number if the apex of the triangle is: (a) at the bottom; (b) at the top.

Question 2 Water flows at 1.6 m³ s¹ through a long rectangular drain of width 0.8 m and streamwise slope 1.25%. Manning's roughness coefficient may be taken as n = 0.013 m-1/3 s. (a) Find the depth of flow in the drain. At one point the drain opens out abruptly into a broader channel of width 2.2 m and lower slope, causing an immediate hydraulic jump. (b) Estimate the depth of flow and Froude number just downstream of the hydraulic jump.

Question ( 2- 26 ) , MCQ 2 Simplity the Navier-Stokes equation as much as possible for the case of incompressible hydrostatics, with gravity acting in the negative z-direction. Begin with the incompressible vector form of the Navier-Stokes equation and identify the final vector equation.

Question 1 Water of density p flows past a smooth flat plate of length L and large span and a laminar boundary layer of thickness d develops on each side. The upstream velocity may be assumed to have the uniform value Uo, whilst the downstream velocity profile has the form: where y is the distance perpendicular to the plate. There is negligible pressure change along the length of the plate. A suitable control volume to analyse the problem is shown below. Depth H is any depth greater than the downstream boundary-layer thickness and cancels during your working. (a) Use continuity to calculate the apparent displacement of streamlines d* (this is called the displacement thickness) as a function of boundary-layer depth d (b) Calculate the difference between momentum fluxes (per unit span) at inlet and outlet of the control-volume shown (c) Hence deduce the viscous drag force (per unit span) on one side of the plate. (d) Noting that there is a boundary layer on both sides of the plate, define a suitable overall drag coefficient and calculate its value. (e) Explain, with reference to the appropriate concepts and definitions of fluid mechanics, how the solution to the above questions would change should the plate be inlined downwards 30° to the horizontal.

Question 2 A circular water tank, 3m in diameter, tapers into a cone as shown in the figure below. It is open to the atmosphere at the top. The tank is used to store water and distribute it to a local town. It is supplied with water through a horizontal pipe 200 m long and 220 mm diameter. A pump feeds the pipe and maintains a constant gauge pressure of 150 kPa at the entry to the pipe. The pipe may be assumed to have a constant friction factor A = 0.02 and losses other than those due to wall friction may be neglected. The tank discharges water to the town through an opening at the base of the cone, that has a diameter of 300 mm and a Cd = 0.68. Assuming the outflow is closed: (a) What is the piezometric head maintained by the pump at the inlet to the pipe? (b) Write an expression for the frictional head loss along the pipe due to a flow rate Q, and hence find an expression for Q when the water level of the tank is a height h above the pipe If the tank is filled to a height of 7 m prior to the outflow being opened: (c) Find the time taken for the water level to reduce to 2 m, assuming the inflow is maintained throughout.

Objective This exercise allows us to observe the load losses of a current that circulates through a widening of 25/40 mm.

Question 4 A trapezoidal channel, with vertical sides, has the geometry shown in the figure below. The bed slope is 1 in 500. Local engineers need to undertake repair works on the channel. The proposed materials to be used are smooth concrete and brickwork. The engineers wish to ensure that the height of the water in the channel, outside of storm surges, never exceed the depth of the trapezoidal section of the pipe, and the design flow rate for normal operations is 80 m³s-¹. (a) Using the appropriate Manning's coefficient for each material, state, with reasons, which of the two materials is best suited to perform the repair works required. Due to climate change, it is predicted that the required flow rate in the channel during extreme rainfall events will increase to 200 m³s-¹. (b) Check that the existing channel is of sufficient size to cope with the predicted increase in required capacity.

2. For the tank shown below, determine the reading of bottom pressure gage in psi if the top of the tank is sealed. The top gage reads -10.8 psi, and the depth of the oil is 6.25 ft.

Q1. A rectangular channel b= 1.5m , Q= 900L/s, the depth of flow before the hump is 1m and Az=200mm , compute the depth of flow above the hump.

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