Lastchance toredeem my terrible drawings! _ swana- 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 maln Ilnes (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 suppEy to a house, other lines branch off to toilets, showers, faucets, etc. The pressure lo 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: d1 = 2.5 m d2 = 5.08 cm d3 = 2.54 cm h, = 30 m h2 = 4.6 m Q2 : 0.0017 m3g'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 Pwater = 1000 kg/m3, and you can assume the velocity at point 1 is O. Hint: Recall that the flow rate Q is the product of the velocity of the ow and the area of the pipe. P2: 393,647 Jg Pa b) Now you can calculate the velocity at point 3. Assuming the flow is incompressible, you can invoke the continuity equation. v3 : x336 (~52 m/s c) What is the pressure at point 3, in both Pascals and psi (pounds per square inch)? P3 = [343,275 " 3: Pa P3 = 49.?7 3: psi Fluids will flow from high to low pressure, so as long as the pressure at the tap ls above 1 atm, openlng the tap should glve water! Most household water lines range from 30-80 psi. Aerators, friction in pipes, and the interface of water hitting 1 aim of air pressure upon exiting the faucet reduces flow to a federally regulated 12.2 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?)