Review CEEN 598D: Fluid Mechanics for Hydro Systems Lindsay Bearup [email protected] Berthoud Hall 121 CEEN 598D– Fall 2015 Exam 2 hours, 8 independent quesFons Only non-­‐graphing calculators will be permiLed I will give you all necessary constants etc. Know the following equaFons with appropriate assumpFons: –  Bernoulli’s EquaFon –  Energy EquaFon (work/head relaFonships will be provided) –  ConFnuity EquaFon –  Reynolds & Froude Numbers •  Review equaFon sheet… • 
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CEEN 598D– Fall 2015 Concept Review -­‐ Mannings EquaFon Vx = −
S0,x
n
2/3
h
R
V = velocity [L/T] S0,x = bed slope [-­‐] Rh = hydraulic radius [L] n = roughness coefficient in [s/m1/3] if not using metric must use a factor, k = 1.49 CEEN 598D– Fall 2015 Energy of Open Channel Flow •  What term drops out from our energy equaFon? •  Know how to determine if something is supercriFcal or subcriFcal •  Will not ask you to find roots or draw the specific energy diagrams (hint hint) CEEN 598D– Fall 2015 EGL & HGL review • For staFonary bodies such as reservoirs or lakes, the EGL and HGL coincide with the free surface of the liquid. The elevaFon of the free surface z in such cases represents both the EGL and the HGL since the velocity is zero and the staFc (gage) pressure is zero. • The EGL is always a distance V2/2g above the HGL. These two curves approach each other as the velocity decreases, and they diverge as the velocity increases. The height of the HGL decreases as the velocity increases, and vice versa. • In an idealized Bernoulli-­‐type flow, EGL is horizontal and its height remains constant. This would also be the case for HGL when the flow velocity is constant . • For open-­‐channel flow, the HGL coincides with the free surface of the liquid, and the EGL is a distance V2/2g above the free surface. • At a pipe exit, the pressure head is zero (atmospheric pressure) and thus the HGL coincides with the pipe outlet (locaFon 3 on Fig. 12–14). • The mechanical energy loss due to fricFonal effects (conversion to thermal energy) causes the EGL and HGL to slope downward in the direcFon of flow. The slope is a measure of the head loss in the pipe. CEEN 598D– Fall 2015 What is the difference in the HGL & EGL of these two systems? CEEN 598D– Fall 2015 What is the difference in the HGL & EGL of these two systems? CEEN 598D– Fall 2015 Review QuesFon 1 Your car runs out of gasoline, and it becomes necessary to siphon gas out of the car of a Good Samaritan. The siphon is a small-­‐diameter hose, and to start the siphon it is necessary to insert one siphon end in the full gas tank, fill the hose with gasoline via sucFon, and then place the other end in a gas can below the level of the gas tank. The difference in pressure between point 1 (at the free surface of the gasoline in the tank) and point 2 (at the outlet of the tube) causes the liquid to flow from the higher to the lower elevaFon. Point 2 is located 0.75 m below point 1 in this case, and point 3 is located 2 m above point 1. The siphon diameter is 5 mm, and fricFonal losses in the siphon are to be disregarded. The density of gasoline is 750 kg/m3. The density of gasoline is 750 kg/m3. a)  What is the minimum Fme to with-­‐ draw 4 L of gasoline from the tank to the can? b)  What is the pressure at point 3? c)  Draw the EGL & HGL for this system. CEEN 598D– Fall 2015 Answer 1 CEEN 598D– Fall 2015 CEEN 598D– Fall 2015 Review QuesFon 2 Water backs up behind a concrete dam as shown. Leakage under the foundaFon gives a pressure distribuFon under the dam as indicated. If the water depth, h, is to great, the dam will topple over about its toe (A). Determine the maximum water depth if l=20 q. Specific weight of concrete = 150 lb/q3 CEEN 598D– Fall 2015 CEEN 598D– Fall 2015 CEEN 598D– Fall 2015 CEEN 598D– Fall 2015 Review QuesFon 3 In a hydroelectric power plant, 100 m3/s of water flows from an elevaFon of 120 m to a turbine, where electric power is generated (Fig. 12–32). The total irreversible head loss in the piping system from point 1 to point 2 (excluding the turbine unit) is determined to be 35 m. If the overall efficiency of the turbine–generator is 80 percent, esFmate the electric power output. CEEN 598D– Fall 2015 Answer 3 CEEN 598D– Fall 2015