A LEVEL PROBLEMS
1) The diagram shows a Venturi meter
installed in a water main. The pipe has a circular cross-section at all
points of the meter, and has diameters D1 = 2.00 m (in
the first segment of the tube), and D2 = 0.80 m in the
second segment of the tube. The mass density of water is r
= 1.0 x 103 kg/m3. Answer
the following questions given that the water in the pipe is flowing at
a volume flow rate R = 0.855 m3/s.
a) What is the speed v1 in the first
section of the pipe, and the speed v2 in the second section
of the pipe? What is the mass rate of flow in the tube?
b) What is the difference in the water
level Dh in
the two tubes?
2) A solid sphere (V = 4pR3/3)
of radius R = 2.00 m and average mass density rs=
.230 g/cm3 is completely submerged
in a tank filled with a fluid of density rf
= .550 g/cm3. It
is held in place by a string attached to the bottom of the tank (see figure).
a) What is the tension, T, of the string?
b) What is the magnitude of the buoyant force
acting on the sphere?
3) How many cubic meters of helium are required
to lift a balloon with a 400 kg payload to a height of 8000 m? (rHe
= 0.18 kg/m3). Assume the balloon maintains a constant
volume and that the density of air decreases with altitude z according
to rair
= roe(-z/8000),
where z is in meters, and ro
= 1.29 kg/m3 (density of air at sea level).
[answer: 1430 m3 ]
4) A large storage tank is filled to a height
ho. If the tank is punctured at a height h from the bottom
of the tank, how far from the tank will the stream land?
[answer: x = vxt = 2[h(ho
- h)]1/2 ]