2. A cylindrical tank of diameter D contains liquid to an initial height h0. At time t = 0 a small stopper of diameter d is removed from the bottom. Using Bernoulli's equation with no losses: • Calculate a differential equation for the free surface height h (t) during draining Determine an expression for the time to to drain the entire tank. • D 1 h(t) Fig.2.The depletion of a cylindrical tank
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- A cylindrical tank with a large diameter is filled with water to a depth D = 0.402 m. A hole of cross-sectional area A = 5.26 cm2 in the bottom of the tank allows water to drain out. (a) What is the rate at which water flows out, in cubic meters per second? (b) At what distance below the bottom of the tank is the cross-sectional area of the stream equal to one-half the area of the hole?14. Through a refinery, fuel ethanol is flowing in a pipe at a velocity of 1 m/s and a pressure of 101300 Pa. The refinery needs the ethanol to be at a pressure of 2 atm (202600 Pa) on a lower level. How far must the pipe drop in height in order to achieve this pressure? Assume the velocity does not change. (Hint: Use the Bernoulli equation. The density of ethanol is 789 kg/m3 and gravity g is 9.8 m/s2Question 1) The circular cross section tank with a height of (0,721 +0,221 +1,521=2.4+3*0,021) m and a radius of 321mm is filled with 1,521 m deep water. Water in the tank is rotating around its axis with an angular speed of 12,1 rad/s, water at a mass flow rate of 12,1 kg/s is added. i) Find the time required for the water not to overflow from the tank ii) Find the hydrostatic force applied to the lateral surface between A-B points at Dt = 3,21 sec. The temperature of the water in the tank and discharge is 15 oC. Solve the problem by making the necessary assumptions and drawing the schematic figure. a=2b=1
- A fully-filled open storage tower of height 32 m and diameter 3.0m supplies water to a house. A horizontal pipe at the base of the tower has a diameter of 2.54cm. To satisfy the needs of the home, the supply pipe must be able to deliver water at a rate of 0.67 gal/s. a. If water were flowing at the maximum rate, what would be the pressure in the horizontal pipe?b. A smaller pipe, of diameter 1.27 cm supplies the second floor of the house, a distance of 7.2 m above the ground level. What are the flow speed and water pressure in this pipe?A sphere, 1 m internal diameter and 6mm wall thickness, is to be pressure-tested for safety purposes with water as the pressure medium. Assuming that the sphere is initially filled with water at atmospheric pressure, what extra volume of water is required to be pumped in to produce a pressure of 3 MN/m2 gauge? For water, K = 2.1 GN/m2. For the material of the sphere E = 200 GN/m2, v = 0.3 and the yield stress 0, in simple tension = 280 MN/m2. a. 0.948 x 10-3 m3b. 0.648 x 10-3 m3c. 0.848 x 10-3 m3d. 0.748 x 10-3 m3Problem 1 •Through a refinery, fuel ethanol is flowing in a pipe at a velocity of 1 m/s and a pressure of 101300 Pa. The refinery needs the ethanol to be at a pressure of 2 atm (202600 Pa) on a lower level. How far must the pipe drop in height in order to achieve this pressure? Assume the velocity does not change. (Hint: Use the Bernoulli equation. The density of ethanol is 789 kg/m3 and gravity g is 9.8 m/s2.Pay attention to units!)
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- The water of a 14’ × 48’ metal frame pool can drain from the pool through an opening at the side of the pool. The opening is about h = 1.05 m below the water level. The capacity of the pool is V = 3740 gallons, the pool can be drained in t = 10.2 mins. P0 is the pressure of the atmosphere. ρ is the density of the water. a. Write the Bernoulli’s equation of the water at the top of the pool in terms of P0, ρ, h. Assuming the opening is the origin. b. Write the Bernoulli’s equation of the water at the opening of the pool in terms of P0, ρ, h and v, where v is the speed at which the water leaves the opening. Assuming the opening is the origin. c. Express v2 in terms of g and h. d. Calculate the numerical value of v in meters per second. e. Express the flow rate of the water in terms of V and t. f. Express the cross-sectional area of the opening, A, in terms of V, v and t. g. Calculate the numerical value of A in cm2A cylindrical tank of diameter D contains liquid to an initialheight h 0 . At time t = 0 a small stopper of diameter d isremoved from the bottom. Using Bernoulli’s equation withno losses, derive ( a ) a differential equation for the freesurfaceheight h ( t ) during draining and ( b ) an expressionfor the time t 0 to drain the entire tank.2. A hydro-electric plant having 50 km2 reservoir area and 100 m head is used to generate power. The energy utilized by the consumers whose load is connected to the power plant during a five hour period is 13.5 x 106 kW-hr. The over-all generation efficiency is 75 %. Find the fall in the height of water in the reservoir after the 5 hour period. show Complete Solution/s (i.e. transformations, equivalent formula, etc).