An enclosed tank containing a liquid of density p has a hole in its side at a di
ID: 1377039 • Letter: A
Question
An enclosed tank containing a liquid of density p has a hole in its side at a distance i from the tank?s bottom (see figure). The hole is open to the atmosphere, and its diameter is much smaller than the diameter of the tank. The air above the liquid is maintained at a pressure P. Determine the speed of the liquid as it leaves the hole when the liquid?s level is a distance h above the hole. Conceptualize Imagine that the tank is a fire extinguisher. When the hole is opened, liquid leaves the hole with a certain speed. If the pressure P at the top of the liquid is increased, the liquid leaves with a higher speed. If the pressure P falls too low, the liquid leaves with a low speed and the extinguisher must be replaced. Categorize Looking at the figure, we know the pressure at two points and the velocity at one of those points. We wish to find the velocity at the second point. Therefore, we can categorize this example as one in which we can apply Bernoulli?s equation. Point 2 is the surface of the liquid.Explanation / Answer
Height from bottom of tank where hole is located, y1=4.60 m
height from bottom of tank of water surface , y2=8.60 m
1 atm is the equivalent of 10.3 m of height of fresh water
The total pressure difference across 'hole' in terms of 'atm' is:
h=(P-P0)+(y2-y1)=(1.25-1)atm+(8.60-4.60) m
h = 0.25 atm + (4) m = 0.25 + (4/10.3) atm = 0.6383 atm
h = 0.6383(10.3) = 6.575 m of fresh water
V = ?2gh = ?(2)(9.81)(6.575) = ?129 = 11.35 m/s {speed of water thru hole}
time(t) for water to fall a distance = y1 = 4.60 m is:
t = ?2(y1)/g = ?(9.2)/(9.81) = ?0.9378 = 0.9684 s
Horizontal distance from hole where water stream lands = V