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CE8302 FLUID MECHANICS II year / III Sem Civil Engineering
UNIT 1
FLUID PROPERTIES AND FLUID STATICS
PART – A (2 MARKS)
1. Define fluids.
Fluid may be defined as a substance which is capable of flowing. It has
no definite shape of its own, but confirms to the shape of the containing
vessel.
2. What are the properties of ideal fluid?
Ideal fluids have following
properties
i) It is incompressible
ii) It has zero viscosity
iii) Shear force is zero
3. What are the properties of real fluid?
Real fluids have following
properties
i) It is compressible
ii) They are viscous in nature
iii) Shear force exists always in such fluids.
4. Define density and specific weight.
3
Density is defined as mass per unit volume (kg/m )
Specific weight is defined as weight possessed per unit volume (N/m3)
5. Define Specific volume and Specific Gravity.
Specific volume is defined as volume of fluid occupied by unit mass
3
(m /kg) Specific gravity is defined as the ratio of specific weight of
fluid to the specific weight of standard fluid.
6. Define Surface tension and Capillarity.
Surface tension is due to the force of cohesion between the liquid particles
at the free surface.
Capillary is a phenomenon of rise or fall of liquid surface relative to
the adjacent general level of liquid.
7. Define Viscosity.
It is defined as the property of a liquid due to which it offers resistance to
the movement of one layer of liquid over another adjacent layer.
8. Define kinematic viscosity.
It is defined as the ratio of dynamic viscosity to mass density. (m²/sec)
9. Define Relative or Specific viscosity.
It is the ratio of dynamic viscosity of fluid to dynamic viscosity of water
at 20°C.
10. Define Compressibility.
It is the property by virtue of which fluids undergoes a change in volume
under the action of external pressure.
11. Define Newtonian law of Viscosity.
According to Newton’s law of viscosity the shear force F acting between
two layers of fluid is proportional to the difference in their velocities du
1
CE8302 FLUID MECHANICS II year / III Sem Civil Engineering
and area A of the plate and inversely proportional to the distance between
them.
12. What is cohesion and adhesion in fluids?
Cohesion is due to the force of attraction between the molecules of the
same liquid.
Adhesion is due to the force of attraction between the molecules of two
different liquids or between the molecules of the liquid and molecules of
the solid boundary surface.
13. State momentum of momentum equation?
It states that the resulting torque acting on a rotating fluid is equal to
the rate of change of moment of momentum
14. What is momentum equation
It is based on the law of conservation of momentum or on the momentum
principle It states that,the net force acting on a fluid mass is equal to the
change in momentum of flow per unit time in that direction.
PART – B(16 MARKS)
1. What are the gauge pressure and absolute pressure at a point 3 m below the free
3 3
surface of a liquid having a density of 1.53x10 kg/m if the atmospheric pressure is
equivalent to 750 mm of mercury? The specific gravity of mercury is 13.6 and
3
density of water is 1000 kg/m .
Solution
Depth of liquid, Z = 3 m
1 3 3
Density of liquid, ρ1 = 1.53x10 kg/m
Atmospheric pressure head, Z = 750 mm of Hg
0
= 0.75 m of Hg
Atmospheric pressure, P = ρ x g x Z
atm 0 0
= (13.6 x 1000) x 9.81 x 0.75
2
= 100062 N/m
Pressure at a point at a depth of 3 m from the free surface of a liquid
P = ρ x g x Z
1 1
= (1.53 x 1000) x 9.81 x 3
2
= 45028 N/m
2
Gauge pressure, P = 45028 N/m
Absolute pressure, = Gauge pressure + Atmospheric pressure
= 45028 + 100062
2
= 145090 N/m
2. Figure shows a conical vessel having its outlet at A to which a U-tube manometer is
connected. The reading of the manometer given in the figure shows when the vessel
is empty. Find the reading of the manometer when the vessel is completely filled
with water.
Solution
Difference of mercury level, h = 20 cm
2
Sp. Gravity of mercury , S2 = 13.6
Sp. Gravity of water, S1 = 1
Density of mercury, ρ2 = 13.6 x 1000
Density of water, ρ1 = 1 x 1000
Equating the pressure above the datum line X-X
2 2015 - 2016
CE8302 FLUID MECHANICS II year / III Sem Civil Engineering
Ρ x g x h = ρ x g x h
2 2 1 1
(13.6 x 1000) x 9.81 x 0.2 = 1000 x 9.81 x h1
h = 2.72 m of water
1
Pressure in left limb = Pressure in right limb
13.6 x 1000 x 9.81 x (0.2 + 2y/100) = 1000 x 9.81 x (3 + h + y/100)
1
(27.2y – y)/100 = 3.0
y = 11.45 cm
The difference of mercury level in two limbs,
= (20 + 2y) cm of mercury level
= 20 + (2 x 11.45)
= 42.90 cm of mercury
Reading of manometer = 42.90 cm
3. Determine the total pressure on a circular plate of diameter 1.5 m which is placed
vertically in water in such a way that the center of the plate is 3 m below the free
surface of water. Find the position of centre of pressure also.
Solution
Diameter of plate, d = 1.5 m
2 2
Area, A = (Π/4) x 1.5 = 1.767 m
h = 3.0 m
Total pressure,F = ρ x g x A x h
= 1000 x 9.81 x 1.767 x 3
= 52002.81 N
Position of centre of pressure, h* = (IG/Ah) + h
IG = (Π x d4)/64
4
= 0.2485 m
h* = (0.2485/(1.767 x 3)) + 3
Position of centre of pressure = 3.0468 m
4. A vertical sluice gate is used to cover an opening in a da m. The opening is 2 m
wide and 1.2 m high. On the upstream of the gate, the liquid of Sp.gr 1.45 lies upto
a height of 1.5 m above the top of the gate, whereas on the downstream side the
water is available upto a height touching the top of the gate. Find the resultant force
acting on the gate and position of centre of pressure. Find also the force acting
horizontally at the top of the gate which is capable of opening it. Assume that the
gate is hinged at the bottom.
Solution
Width of gate, b = 2 m
Depth of gate, d = 1.2 m
2
Area, A = (2 x 1.2) = 2.4 m
Sp. gr of liquid = 1.45
3
Density of Density, ρ1 = 1.45 x 1000 = 1450 kg/m
Let F = Force exerted by the fluid of sp. gr 1.45 on gate
1
F = Force exerted by water on gate
2
F = ρ x g x A x h
1 1 1
h = Depth of C.G of gate from free surface of liquid
1
= 1.5 + (1.2/2)
= 2.1 m
CE8302 FLUID MECHANICS II year / III Sem Civil Engineering
F = 1450 x 9.81 x 2.4 x 2.1 = 71691 N
1
F = ρ x g x A x h
2 2 2
3
Ρ2 = 1 x 1000 kg/m
h = 1.2/2 = 0.6 m
2
F = 1000 x 9.81 x 2.4 x 0.6 = 71691 N
2
(i) Resultant force on the gate = F - F = 71691 – 14126 = 57565 N
1 2
(ii) Position of centre of pressure of resultant force
The force F will be acting at a depth of h * from free surface
1 1
of liquid, given by the relation,
h * = (I /A h ) + h
1 G 1 1
3 3 4
IG = bd /12 = 2 x 1.2 /12 = 0.288 m
h * = 0.288 / (2.4 x 2.1) + 2.1 = 2.1571 m
1
Distance of F from hinge,
1
= (1.5 + 1.2) - h * = 2.7 – 2.1571 = 0.5429 m
1
h * = (I /A h ) + h
2 G 2 2
= (0.288/2.4 x 0.6) + 0.6 = 0.8 m
Distance of F from hinge = 1.2 – 0.8 = 0.4 m
2
The resultant force 57565 N will be acting at a distance given by
= ((71691 x 0.5429) – (14126 0.4))/57565
= 0.578 m above the hinge
(iii) Force at the top of gate which is capable of opening the gate
F x 1.2 + F x 0.4 = F x 0.5429
2 1
F = ((71691 x 0.5429)- (14126 x 0.4))/1.2
F = 27725.5 N
5. A block of wood of specific gravity 0.7 floats in water. Determine the meta-centric
height of the block if its size is 2 m x 1 m x 0.8 m.
Solution
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