fluid tutorial 2_ans dr.waleed. 01004444149
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Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (1)
Tutorial (2)
(1) A spherical balloon with a diameter of 6 m is filled with helium at 20 oC
and 200 πππ. Determine the mole number and the mass of the helium in
the balloon
Solution
P Pressure Pa
V Volume m3
N Number of moles kmol
Ru Universal gas constant J/kmol.K
T Temperature K
Rg Gas constant J/kg.K
M Molar mass Kg/kmol
m Mass kg
(
)
For helium (M=4 kg/kmol)
m = 9.28 x 4 = 37.1 kg
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (2)
(2) The pressure in an automobile tire depends on the temperature of the air
in the tire. When the air temperature is 25 oC, the pressure gage reads 210
πππ. If the volume of the tire is 0.025 π3, Determine the pressure in the tire
when the air temperature in the tire rises to 50 oC. Also, determine the
amount of air that must be bled off to restore pressure to its original value
at this temperature. Assume the atmospheric pressure to be 100 πππ.
Solution
The absolute pressure in the tire is
T1 = 25 +273 = 298 K
T2 = 50 +273 = 323 K
Assume the tire volume is constant (also the mass)
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (3)
(3) It is observed that the density of an ideal gas is increased by 10% when
compressed isothermally from 10 ππ‘π to 11 ππ‘π. Determine the percent
increase in density of the gas if it is compressed isothermally from 100 ππ‘π
to 101 ππ‘π.
Solution
For ideal gas
(
) (
)
(
)
(
)
β
At P = 10 atm
At P = 100 atm
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (4)
(4) What pressure must be applied to water (πΈπ£ = 2.2 Γ 109 ππ) to reduce its
volume by 1%?
Solution
β
β
β
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (5)
(5) Eight kilometers below the surface of the ocean, the pressure is 81.7πππ.
Determine the specific weight of the sea water at this depth if the specific
weight at the surface is 10.06 πΎπ/π3 and the average bulkβs modulus of
elasticity is 2.34 πΊππ. Assume that π does not change significantly.
Solution
ππ π β
Depth = 8 km
π πππ
π£
π
π£
π ππβ
π£
π£
π
πΎ
π£ π£ π£
π£ π£
π£
π π
πΎ
π£ π£ π π
πΎ
π£
π£ π£ π£
π£
π
π£
π π β
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (6)
(6) Calculate the velocity of sound in water at 20 oC ,(πΎ = 2.2 10
9 ππ).
Solution
βπΎ
β
π β
(7) Calculate the velocity of sound in air at 0
oC, πabs= 101.3 πππ.
Solution
βπΎ β π β
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (7)
(8) A thin plate moves between two parallel, horizontal flat surfaces at a
constant velocity of 5 π/ . The two surfaces are spaced 4 ππ apart, the plate
is 1ππ apart from the top surface and the medium between them is filled
with oil whose viscosity is 0.9 π. /π2. the part of the plate immersed in oil
at any given time is 2 π long and 0.5 π wide. If the plate moves between the
surfaces. Determine the force required to maintain this motion if
(a) Both upper and lower surfaces are stationary.
(b) The upper surface moves at velocity = 2 π/ in the same direction as Plat
where the lower surface remains stationary.
Solution
The magnitudes of shear forces acting on the upper and lower surfaces of the plate are
|
|
π
π
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (8)
π
π
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (9)
(9) Fluid flow through a circular pipe is one-dimensional, and the velocity
profile for Laminar flow is given by
, where is the
radius of the pipe, π is the radial distance from the center of the pipe, and
max is the maximum flow velocity, which occurs at the center.
Given that = 0.08 π, max= 3 π/ and ΞΌ = 0.001ππ/π.
Determine:
(a) The shearing stress acting on the pipe wall.
(b) The shearing stress acting on a plane parallel to the pipe walls and passing
through the centerline (mid-plane).
(c) Given the pipe length= 30 π, calculate the drag force applied by the fluid
on pipe.
Solution
π ( π
)
π|
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (10)
π(
π
)
π
π π β
Along the mid-plane r = 0
so
(
)
π
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (11)
(10) 10. A 25 mm-diameter shaft is pulled through a cylindrical bearing as
shown in the figure. The lubricant that fills the 0.3 ππ gap between the shaft
and bearing is an oil having a kinematic viscosity of 8.0 Γ 10β4
and a specific
gravity of 0.91. Determine the force π required to pull the shaft at a velocity of
3 π/ . Assume the velocity distribution in the gap is linear.
Solution
β
π
π£ π π‘ π π‘
ππ π‘
π£
πΊ
π
π£
π
π π
Tutorial (2) Dr.waleed, Mob. 0100 4444 149 Page (12)
(11) The viscosity of a fluid is to be measured by a viscometer constructed of
two 40 ππ long concentric cylinders as shown in the figure. The outer
diameter of the inner cylinder is 12 ππ, and the gap between the two
cylinders is 10 ππ. The inner cylinder is rotated at 300 πππ, and the torque
is measured to be 1.8 N.m, Determine the viscosity of the fluid.
Solution
π£ π π‘ π π‘
ππ π‘
π£
π£
(
)
(
)
(
)
(
β ) π π β