A. A cylindrical tank of radius R , filled to the top with a liquid, has a small

Question

A. A cylindrical tank of radius R , filled to the top with a liquid, has a small hole in the side, of radius r , at distance d below the surface. Find an expression for the volume flow rate through the hole.

Express your answer in terms of the variables d , r , R , and appropriate constants.

B. A 3.0-mm -diameter hole is 1.0m below the surface of a 2.0-m -diameter tank of water. What is the rate, in mm/min , at which the water level will initially drop if the water is not replenished?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a)
the equation of pressure is
?gd=1/2?v^2
v=sqrt(2gd)
the flow is
?=v*S
?=?r^2*sqrt(2gd)

b)
v=sqrt(2gd)

=sqrt(2*9.8*0.003)
v=0.24 m/s
?=v*S
?=0.24*3.0x10^-3
?=7.2x10^-2 m^3/s
volume of tanks is
V=3.14 m^3
surface of tank is
S=3.14 m^2
the rate at which the water level will initially drop is
R=?/S
R=7.2x10^-2/3.14=2.29x10^-2 m/s
R=22.9 mm/s

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