Tutorial_Fluid Mechanics
• Problem 1
Consider a U-tube whose arms are open to the atmosphere. Now water
is poured into the U-tube from one arm, and light oil (ρ = 790 kg/m3)
from the other. One arm contains 70-cm-high water, while the other arm
contains both fluids with an oil-to-water height ratio of 6.
Determine the height of each fluid in that arm.
Water
oil
ha
hw1
hw2
SAME FLUID, SAME LEVEL, SAME PRESSURE
Problem 2
Freshwater and seawater flowing in parallel horizontal pipelines are
connected to each other by a double U-tube manometer, as shown in Figure.
hw = 60 cm; hhg = 10 cm; hair = 70 cm; hsea = 40 cm.
Determine the pressure difference between the two pipelines.
Take the density of seawater to be 1035 kg/m3. Can the air column be
ignored in the analysis?
Air
hsea
hair
Sea
water
Fresh
water
hw
hHg
Mercury
Problem 3
The gauge pressure of the air in the tank shown in Figure is measured to
be 65 kPa. hw = 30 cm; hhg = h cm; hoil = 75 cm. ρoil = 720 kg/m3 and ρHg =
13,600 kg/m3.
Determine the differential height h of the mercury column.
65 kPa
Air
hoil
Water
hw
hHg
Problem 4
The top part of a water tank is divided into two compartments as shown
in Figure. Now a fluid with an unknown density is poured into one side,
and the water level rises a certain amount on the other side to
compensate for this effect.
Based on the final fluid heights shown on the figure, determine the
density of the fluid added. Assume the liquid does not mix with each
other.
Unknown
fluid
Water
80 cm
45 cm
50
cm
Problem 5
Two chambers with the same fluid at their base are separated by a
piston whose weight is 25 N, as shown in figure.
Calculate the gauge pressures in chambers A and B.
Pison
A
air
air
B
D
50 cm
30 cm
C
30 cm
E
water
90 cm
25 cm
Problem 6
A gasoline line is connected to a pressure gauge through a double-U
manometer, as shown in figure. If the reading of the pressure gauge is
370 kPa, determine the gauge pressure of the gasoline line. S.G. of
gasoline = 0.7; S.G. of Hg = 13.6; S.G. of oil = 0.79
Pgage = 370 kPa
Oil
45 cm
Gasoline
Pipe
Air
22 cm
50 cm
10 cm
Water
Mercury
Problem 7
A double inverted U-tube manometer containing oil (SG = 0.8), mercury
(SG = 13.6) and water is used to measure large pressure difference
between gas in pipe B and gasoline in pipe A as shown in figure.
Knowing that h1 = 60 cm, h2 = 87 cm, h3 = 35 cm, and h4 = 24 cm,
determine the presure difference between A and B. Neglect the gas
density and use γwater = 9810 N/m3 for water.