A river has a cross section that is approximately a rectangle 10 feet deep and 5

Question

A river has a cross section that is approximately a rectangle 10 feet deep and 50 feet wide. The average velocity is 1 ft/s. How many gallons per minute pass a given point? What is the average velocity at a point downstream, where the channel shape has changed to 7 feet in depth and 150 feet in width? In March 1996 a special release of water, Q = 45,000 ft^3/s, was made from the Glen Canyon Dam, to create an artificial flood in the Grand Canyon. If the flow was through 8 pipes, each with an internal diameter of 8 feet, estimate the velocity through those pipes. A tank contains 1000 m^3 of a salt solution, with salt concentration = 10 kg/m^3. At time zero, salt free water starts to flow into the tank at a rate of 10 m^3/min. Simultaneously, salt solution flows out of the tank at 10 m^3/min, so that the volume of solution in the tank is always 1000 m^3. A mixer in the tank keeps the concentration of salt in the entire tank uniform so that the concentration in the effluent is the same as the concentration in the tank. What is the concentration in the effluent as a function of time? A cylindrical tank is 3 m in diameter, with axis vertical, has an influent line of 0.1 m inside diameter and an outflow line of 0.2 m inside diameter. Water is flowing in the inflow line at a velocity of 2 m/s and leaving by the outflow line at 1 m/s. Is the level in the tank rising or falling? How fast? A vacuum pump operates at a constant volumetric flow rate of 10 liters/min based upon pump inlet conditions. How long will it take to pump down a 100 L tank containing air from 1 atm to 0.01 atm, assuming that the temperature is constant?

Explanation / Answer

1 ) Cross sectional area = 10X50 = 500 sq ft

velocity = 1ft/s

flow through a point = 500 ft3/s

= 224416 gallons/minute

Cross section at the point downstream = 7X 150 = 1050 sq ft

velocity at the point = 0.476 ft/s

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