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Answer :
Final answer:
The process involved in finding the rate of discharge in a cylindrical tank involves calculating the area of the discharge pipe and the rate of the fluid being discharged. After converting the given rates into the required units, we substitute these values into the fluid dynamics flow rate formula to find the discharge rate, which in this case is approximately 3.42 cubic feet per second.
Explanation:
To find the rate of discharge of water in a cylindrical vertical tank, you use the principle of fluid flow rate in the field of fluid dynamics. In fluid dynamics the fluid flow rate or volume flow rate, represented by Q, is the volume of fluid which passes through a given surface per unit time. In this case, it can be determined by the equation: Q = Ad/t = Av where A is the area and v is the velocity.
Firstly, we find the cross-sectional area of the discharge pipe which has a diameter of 6 inches (or 0.5 feet). The cross-sectional area can be given by A=πr², where r is the radius (0.25 feet), so we get A = 3.14*(0.25)² = 0.196 ft².
Next, since we know the tank is discharging at 300 gallons per minute (gpm), we must convert this to cubic feet per second as requested. Since 1 gallon = 0.133681 cubic feet and 1 minute = 60 seconds, we have a discharge rate of (300*0.133681/60) = 0.67 cubic ft/sec.
Subsequently, we can substitute the values into Q = Av to solve for v (the velocity). With Q = 0.67 cubic ft/sec and A = 0.196 ft², we can find v (velocity) = 0.67/0.196 = 3.42 ft/s.
Therefore, the rate of discharge in cubic feet per second from the tank through a 6-inch diameter pipe is approximately 3.42 ft/s.
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