Fluid mechanics problem set 1
1. (a) Find the altitude (in meters) where the density of air has fallen to half its value
at sea level.
(b) Find the altitude (in meters) where the pressure has fallen to half its value at sea level.
(c) Why is the answer to part (a) different from the answer to part (b)?
2. The pressure at any point in the atmosphere is equal to the total weight of the air
above that point, per unit area. Given that the atmospheric pressure at sea level is about
105 Pa, and the radius of the earth is 6370 km, estimate the mass of all the air contained
in the atmosphere.
3. In a hydraulic press, a force of 200 N is exerted on the small piston (area 10 cm2).
Determine the force exerted by the large piston (area 100 cm2), if the two pistons were at
the same height.
4. For the hydraulic press described in the previous problem, what is the force
produced by the large piston if it were located 2 m above the small piston? The density of
the hydraulic fluid is 920 kgm3.
5. Two cylinders of cross-sectional areas A1 and A2 are joined by a connecting passage,
as shown in figure. A force F1 acts on one piston, and a force F2 acts on the other. Find
F2 in terms of F1, A1, A2, ρ, g and H, where ρ is the fluid density. Ignore the weights of
the pistons.
, Problem set: Hydrostatics
1. An unknown immiscible liquid seeps into the bottom of an open oil tank. Some
measurements indicate that the depth of the unknown liquid is 1.5m and depth of the
oil (specific weight 8.5 kN/m3) floating on top is 5m. A pressure connected to the
bottom of the tank reads 65 kPa. What is the specific gravity of the unknow liquid?
2. Sometimes when riding an elevator or driving up or down a hilly road, a person’s ear
‘pop’ as the pressure difference between inside and outside the ear equalize.
Determine the pressure difference associated with this phenomenon if it occurs during
a 15m elevation change.
3. In the international standard atmosphere, the troposphere extends to the height of
11km, where the pressure is 22.6kPa (abs). In the next layer called the stratosphere,
the temperature is constant at -56.5 oC. Determine the pressure and density in this
layer at 15km.
4. A mercury manometer is connected to a large reservoir of water. Determine the ratio
hw/hm for hw and hw shown in the figure.
5. Two pipes are connected by a manometer as shown in the figure. Determine the pressure
difference, PA-PB, between the pipes.
, 6. For an inclined tube manometer shown in the figure, the pressure in the pipe A is 0.6 psi. The
fluid in both pipes A and B is water, and the gage fluid in manometer has a specific weight of
2.6. What is the pressure in pipe B corresponding to the differential reading shown?
7. An air filled, hemispherical shell is attached to the bottom of the ocean floor at depth 10m as
shown in figure. A mercury barometer located inside the shell reads 765mm Hg, and a
mercury U-tube manometer designed to give outside water pressure indicates a differential
reading of 735mm Hg as illustrated. Based of these data, what is the atmospheric pressure at
the surface of the ocean.
8. An inverted U-tube manometer containing oil (SG = 0.8) is located between two reservoirs as
shown in the figure. The reservoir on the left which contains carbon tetrachloride, is closed,
and pressurized to 8psi. The reservoir on the right contains water and is open to atmosphere.
With the given data, determine the depth of water, h, in the right reservoir
1. (a) Find the altitude (in meters) where the density of air has fallen to half its value
at sea level.
(b) Find the altitude (in meters) where the pressure has fallen to half its value at sea level.
(c) Why is the answer to part (a) different from the answer to part (b)?
2. The pressure at any point in the atmosphere is equal to the total weight of the air
above that point, per unit area. Given that the atmospheric pressure at sea level is about
105 Pa, and the radius of the earth is 6370 km, estimate the mass of all the air contained
in the atmosphere.
3. In a hydraulic press, a force of 200 N is exerted on the small piston (area 10 cm2).
Determine the force exerted by the large piston (area 100 cm2), if the two pistons were at
the same height.
4. For the hydraulic press described in the previous problem, what is the force
produced by the large piston if it were located 2 m above the small piston? The density of
the hydraulic fluid is 920 kgm3.
5. Two cylinders of cross-sectional areas A1 and A2 are joined by a connecting passage,
as shown in figure. A force F1 acts on one piston, and a force F2 acts on the other. Find
F2 in terms of F1, A1, A2, ρ, g and H, where ρ is the fluid density. Ignore the weights of
the pistons.
, Problem set: Hydrostatics
1. An unknown immiscible liquid seeps into the bottom of an open oil tank. Some
measurements indicate that the depth of the unknown liquid is 1.5m and depth of the
oil (specific weight 8.5 kN/m3) floating on top is 5m. A pressure connected to the
bottom of the tank reads 65 kPa. What is the specific gravity of the unknow liquid?
2. Sometimes when riding an elevator or driving up or down a hilly road, a person’s ear
‘pop’ as the pressure difference between inside and outside the ear equalize.
Determine the pressure difference associated with this phenomenon if it occurs during
a 15m elevation change.
3. In the international standard atmosphere, the troposphere extends to the height of
11km, where the pressure is 22.6kPa (abs). In the next layer called the stratosphere,
the temperature is constant at -56.5 oC. Determine the pressure and density in this
layer at 15km.
4. A mercury manometer is connected to a large reservoir of water. Determine the ratio
hw/hm for hw and hw shown in the figure.
5. Two pipes are connected by a manometer as shown in the figure. Determine the pressure
difference, PA-PB, between the pipes.
, 6. For an inclined tube manometer shown in the figure, the pressure in the pipe A is 0.6 psi. The
fluid in both pipes A and B is water, and the gage fluid in manometer has a specific weight of
2.6. What is the pressure in pipe B corresponding to the differential reading shown?
7. An air filled, hemispherical shell is attached to the bottom of the ocean floor at depth 10m as
shown in figure. A mercury barometer located inside the shell reads 765mm Hg, and a
mercury U-tube manometer designed to give outside water pressure indicates a differential
reading of 735mm Hg as illustrated. Based of these data, what is the atmospheric pressure at
the surface of the ocean.
8. An inverted U-tube manometer containing oil (SG = 0.8) is located between two reservoirs as
shown in the figure. The reservoir on the left which contains carbon tetrachloride, is closed,
and pressurized to 8psi. The reservoir on the right contains water and is open to atmosphere.
With the given data, determine the depth of water, h, in the right reservoir
