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Answer :
Final answer:
To determine the rate at which the level of water is rising in the tank, we need to calculate the volume flow rate of water entering the tank through the two pipes.
Explanation:
To determine the rate at which the level of water is rising in the tank, we need to calculate the volume flow rate of water entering the tank through the two pipes. We can use the equation Q = A * v, where Q is the volume flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water.
Given that the flow rate at A is 400 gal/h and at B it is 200 gal/h when d = 6 in, we can convert the flow rates to gallons per second (gal/s) and calculate the cross-sectional areas of the pipes at that specific depth.
Once we have the volume flow rates for the two pipes, we can subtract the flow rate at B from the flow rate at A to determine the net flow rate. This net flow rate will give us the rate at which the level of water is rising in the tank.
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Final answer:
The rate at which the water level in the tank is rising can be found by combining the flow rates from both pipes, converting the volume to cubic feet, and dividing by the cross-sectional area of the tank.
Explanation:
The question is about the rate at which the water level is rising in the tank due to water inflow from two pipes A and B. Here, we need to apply the flow rate concept from Physics, which is the volume of fluid flowing past a point through a certain area per unit time.
Flow rate or volume flow rate is expressed as Q = Av, where A is the cross-sectional area and v is the average velocity. Given that pipe A has a flow of 400 gal/h and pipe B a flow of 200 gal/h, the total flow into the tank is 600 gal/h.
To convert this into a rate at which the water level in the tank is rising, we would need to know the cross-sectional area of the tank. Let's denote the diameter of the tank as 'd'. As the tank has a diameter of 6 inches (or 0.5 feet), we can find the area of the tank using the formula for the area of a circle, A = Pi*(d/2)^2.
Now we can calculate the rate at which the tank level is rising (v), which is the flow rate divided by the tank’s area. This will provide an answer in feet per hour because we converted the volume flow from gallons to cubic feet and the tank diameter from inches to feet.
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