Basic physics problems …. Please help me anyone?
1. A fountain sends water to a height of 200m. What must the pressurization (above atmospheric) of the underground water system? (1 atm = 10 to the 5th power N/m squared.
2. Water is forced out of a fire extinguisher by air pressure. The tank pressure is 455 Kpa. What is the water jet speed when the water level in the tank is 0.5 m below the nozzle?
3. Water flows at 10m/s thru a pipe with a r=.030m. The pipe gies up to the 2nd floor of the building, 2.0 m higher and the pressure remains unchanged. What is the radius of the pipe on the 2nd floor?
These are all Bernoulli’s equation problems.
1/2 (rho)v^2 + (rho) g h + p is constant
1) The water underground has little velocity, and the water at the top of the fountain has little velocity, so you can discount the kinetic energy term. So only the potential contributes to the pressure.
Delta pressure = (rho) g h
They give you the height (h). You know the acceleration due to gravity (g) and the density of water (rho).
2) In this case, you need to use the kinetic and potential terms.
delta pressure = rho g h + 1/2 rho v^2
v = sqrt (2 (delta p) / rho – 2 g h) )
3) The volume flow rate is the same through both pipes. Speed * area is constant. So speed goes like 1 / area which goes like 1 / radius^2.
So speedbottom = speedtop * (radiustop / radiusbottom)^2
Now use Bernoulli’s equation. Pressure is constant, so rho cancels and
vtop^2 + 2 g h = vbottom^2 = vtop * (rtop / rbottom)^2
Solve for the radius of the pipe on the second floor
rtop = sqrt (rbottom^2 * vtop + 2gh / vtop)
Greg gets kicked out with a fire extinguisher
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