Last chance to redeem my terrible drawings! h d3 m dz The simplified image above depicts...

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Last chance to redeem my terrible drawings! h d3 m dz The simplified image above depicts how water towers provide pressure to homes in the surrounding area. A tower maintains a reservoir of water at a constant height, the air above it at atmospheric pressure (i.e., point 1 is at 1 atm; 105 Pa). Water is carried via main lines (large pipes up to a foot or two in diameter, not pictured) to supply lines that branch off toward homes (gray point 2). From a main supply to a house, other lines branch off to toilets, showers, faucets, etc. The pressure in the line allows the water to flow when you open the tap (gray dot/point 3). The following values may be useful in your calculations: d = 2.5 m d2 = 5.08 cm d3 = 2.54 cm h = 30 m h = 4.6 m Q2 =0.0017 m/s. What is the pressure of the water at the tap? To answer these, let's break this question down into pieces. a) Calculate the pressure in the water main (at point 2). The density of water is water = 1000 kg/m, and you can assume the velocity at point 1 is 0. Hint: Recall that the flow rate Q is the product of the velocity of the flow and the area of the pipe. P = Pa b) Now you can calculate the velocity at point 3. Assuming the flow is incompressible, you can invoke the continuity equation. V3 = m/s c) What is the pressure at point 3, in both Pascals and psi (pounds per square inch)? P3 = P3 = Pa psi Fluids will flow from high to low pressure, so as long as the pressure at the tap is above 1 atm, opening the tap should give water! Most household water lines range from 30-80 psi. Aerators, friction in pipes, and the interface of water hitting 1 atm of air pressure upon exiting the faucet reduces flow to a federally regulated 1-2.2 gallons per minute. Multiple household members simultaneously opening taps will reduce the overall pressure among the various lines being used (ever had the toilet flushed while you're in the shower?). Last chance to redeem my terrible drawings! h d3 m dz The simplified image above depicts how water towers provide pressure to homes in the surrounding area. A tower maintains a reservoir of water at a constant height, the air above it at atmospheric pressure (i.e., point 1 is at 1 atm; 105 Pa). Water is carried via main lines (large pipes up to a foot or two in diameter, not pictured) to supply lines that branch off toward homes (gray point 2). From a main supply to a house, other lines branch off to toilets, showers, faucets, etc. The pressure in the line allows the water to flow when you open the tap (gray dot/point 3). The following values may be useful in your calculations: d = 2.5 m d2 = 5.08 cm d3 = 2.54 cm h = 30 m h = 4.6 m Q2 =0.0017 m/s. What is the pressure of the water at the tap? To answer these, let's break this question down into pieces. a) Calculate the pressure in the water main (at point 2). The density of water is water = 1000 kg/m, and you can assume the velocity at point 1 is 0. Hint: Recall that the flow rate Q is the product of the velocity of the flow and the area of the pipe. P = Pa b) Now you can calculate the velocity at point 3. Assuming the flow is incompressible, you can invoke the continuity equation. V3 = m/s c) What is the pressure at point 3, in both Pascals and psi (pounds per square inch)? P3 = P3 = Pa psi Fluids will flow from high to low pressure, so as long as the pressure at the tap is above 1 atm, opening the tap should give water! Most household water lines range from 30-80 psi. Aerators, friction in pipes, and the interface of water hitting 1 atm of air pressure upon exiting the faucet reduces flow to a federally regulated 1-2.2 gallons per minute. Multiple household members simultaneously opening taps will reduce the overall pressure among the various lines being used (ever had the toilet flushed while you're in the shower?).