At time t = 0 the level of water in tank A is two feet above the level of water in tank B (the above image shows the levels at time t = 0). You may assume quasi-steady state conditions – that is – the steady flow in pipe equations are assumed valid at any time – even though the flow rate does change with time (it changes very slowly – so this assumption is allowed). You must account for the frictional effects in the 25 feet of 0.1 inch diameter pipe. You may neglect the frictional effects in the two tanks. Both tanks are open to the atmosphere. The velocity of water through the 0.1 inch diameter pipe will be much faster that the rate of decrease of the water level in tank A (and also much faster than the rate of increase of the water level in tank B). You must confirm laminar flow if you plan to use that in your solution. Choose to set the z = 0 point as the height of the water in tank B when t = 0. You should recognize that flow will occur until the levels in both tanks are the same. You should instantly know what that level will be (relative to where you have chosen to set the z = 0 mark). (a) What is the function zA = f (time)? zA is the height of the water level in tank A. So ... zA begins at 2 feet and decreases to a value that you should sort of already have figured out. I am asking you for the function that explains how zA changes as time increases. Your function may contain zA, t, and numbers. (b) Include a plot of zA (feet) vs. time (seconds).
At time t = 0 the level of water in tank A is two feet above the level of water in tank B (the above image shows the levels at time t = 0). You may assume quasi-steady state conditions – that is – the steady flow in pipe equations are assumed valid at any time – even though the flow rate does change with time (it changes very slowly – so this assumption is allowed). You must account for the frictional effects in the 25 feet of 0.1 inch diameter pipe. You may neglect the frictional effects in the two tanks. Both tanks are open to the atmosphere. The velocity of water through the 0.1 inch diameter pipe will be much faster that the rate of decrease of the water level in tank A (and also much faster than the rate of increase of the water level in tank B). You must confirm laminar flow if you plan to use that in your solution. Choose to set the z = 0 point as the height of the water in tank B when t = 0. You should recognize that flow will occur until the levels in both tanks are the same. You should instantly know what that level will be (relative to where you have chosen to set the z = 0 mark). (a) What is the function zA = f (time)? zA is the height of the water level in tank A. So ... zA begins at 2 feet and decreases to a value that you should sort of already have figured out. I am asking you for the function that explains how zA changes as time increases. Your function may contain zA, t, and numbers. (b) Include a plot of zA (feet) vs. time (seconds).
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