1. A typical garden hose has an inner diameter of 5/8\". Let\'s say you connect
ID: 1784912 • Letter: 1
Question
1. A typical garden hose has an inner diameter of 5/8". Let's say you connect it to a faucet and the water comes out of the hose with a speed of 7.0 feet per second. If you then put your thumb over the end of the hose so the opening is only a circle 0.25" across, with what speed will the water stream out now?
2. If you hold a sheet of paper by one edge so it droops down and then blow horizontally across (not at, but across) the top surface, the paper will actually rise up. Try it!
Let's calculate why this happens. Assume you can blow air at a speed of 6.3 meters per second. Calculate the difference in pressure between the top and bottom of the paper, assuming the ambient air pressure is 1.00 atm and the density of air is 1.22 kg/m3.
If the area of paper over which you are blowing is roughly a rectangle 4.0 cm wide and 7.0 cm long, what is the net force resulting from the pressure difference?
FYI, an 8.5x11" sheet of typical printer paper weighs about 0.045 N.
Explanation / Answer
by continuity equation
area1 * velocity1 = area2 * velocity2
initially inner diameter = 5/8 inch or 0.052 ft
final diameter = 0.25 inch or 0.0208 ft
pi * (0.052 / 2)^2 * 7 = pi * (0.0208 / 2)^2 * velocity
velocity = 43.75 ft/sec
speed of water = 43.75 ft/sec
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