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Density
1. If 5 m3 of certain oil weights 45 kN calculate the specific weight, specific gravity and mass
density of the oil.
2. Certain liquid has a mass density of 1550 kg/m3 calculate its specific weight, specific
gravity and specific volume.
Elasticity:
1. A liquid is undergone a change of pressure from 6.87 MPa to 13.73 MPa to make the
volumetric change of 0.0113m3 to 0.0111m3. What is the bulk modulus of elasticity of the
liquid?
2. If the volume of a liquid is decreased by 0.25% for a change of pressure from 6.5 MN/m2
to 16.1 MN/m2, calculate the bulk modulus of the liquid.
3. At a certain depth of a liquid where the pressure is 850 N/cm2 what will be the change in
specific volume and specific weight with respect to the surface? Given that the specific
weight of that liquid at surface is 1025 N/cm3 and the bulk modulus of elasticity is 24x103
N/cm3.
Viscosity:
1. A plate 0.25 mm distant from a fixed plate moves at 40cm/s and requires a force of
0.25N/m2.Determine the dynamic viscosity of the fluid in between the plates.
2. At a certain point in an oil the shear stress is 0.2 N/m2 and the velocity gradient is 0.21 s-1.
If the mass density of the oil is 950 kg/ m3 find the kinematic viscosity.
3. If a certain liquid has a viscosity of 0.048 poise and kinematic viscosity of 3.50x10-2 stokes
what is the specific gravity of the liquid?
4. A cubical block of 20 cm edge and of 20 kg weight is allowed to slide down along a plane
inclined at 300 to the horizontal on which there is a film of oil having viscosity 2.16x10-3 Ns/m2.What will be the terminal velocity of the block if the film thickness is 0.025mm?
5. If the equation of a velocity profile over a plate is v=2 y2/3(where v is the velocity in m/s)
determine the shear stress at y=0 and at y= 0.075m. Given the viscosity of the liquid is 8.35
poise.
6. A hydraulic lift consists of a 25 cm diameter ram and slides in a cylinder of diameter
25.015 cm while the annular space is being filled up with oil having kinematic viscosity of
0.025cm2/s and specific gravity of 0.85. If the rate of travel of the ram is 9.15m/min find
the frictional resistance when 3.05 m of ram is engaged in the cylinder.
7. A tape of 0.015 cm thick and 1.00 cm wide is to be drawn through a gap with a clearance
of 0.01cm on each side. A lubricant of viscosity 0.021 Ns/m2 completely fills the gap for a
length of 0.8 cm along the tape. If the tape can withstand a maximum tensile force of 7.5 N
determine the maximum speed with which it can be drawn through the gap.
8. Determine the torque and power required to run a 15 cm long and 5 cm diameter shaft
@500 rpm in a 5.1 cm diameter concentric bearing flooded with oil of viscosity 100
centipoise.
9. A thrust bearing having a 12cm diameter pad rotating on another pad separated by an oil
film of 1.5 mm of viscosity 85 centipoise. Compute the power dissipated in the bearing if it
rotates at 150 rpm.
Surface tension:
1. Find the pressure inside a water droplet having diameter of 0.5 mm at 200C if the
outside pressure is 1.03N/cm2 and the surface tension of water at that temperature is
0.0736N/m.
2. The diameters of the two capillaries of a U-tube are 1.0 mm and 1.5 mm
respectively. Now if it is partially filled with water having surface tension of 0.0736
N/m and zero contact angle what will be the difference in the level of miniscii
between the two capillaries.
3. Compare the capillary rise of water and mercury in a glass tube of 2 mm diameter at
200C .Given that the values of surface tension of water and mercury at 200C are
0.0736 N/m and 0.051N/m respectively. Contact angles of water and mercury are 00
and 1300 respectively.
4. Find the excess pressure inside a cylindrical jet of water 4 mm diameter than the
outside atmosphere? The surface tension of water is 0.0736 N/m at that
temperature.
5. Air is forced through a tube of internal diameter of 1.5mm immersed at a depth of
1.5 cm in a mineral oil having specific gravity of 0.85. Calculate the unit surface
energy of the oil if the maximum bubble pressure is 150 N/m2.
Fluid pressure and its measurement:
1. Convert a pressure head of 10 m of water column to kerosene of specific gravity 0.8
and carbon-tetra-chloride of specific gravity of 1.62.
2. Two pipes on the same elevation convey water and oil of specific gravity 0.88
respectively. They are connected by a U-tube manometer with the manometric liquid
having a specific gravity of 1.25. If the manometric liquid in the limb connecting the
water pipe is 2 m higher than the other find the pressure difference in two pipes.
3. A two liquid double column enlarged-ends manometer is used to measure pressure
difference between two points. The basins are partially filled with liquid of specific
gravity 0.75 and the lower portion of U-tube is filled with mercury of specific
gravity 13.6. The diameter of the basin is 20 times higher than that of the U-tube.
Find the pressure difference if the U-tube reading is 25 mm and the liquid in the pipe
has a specific weight of 0.475 N/m3.
4. Water flows through pipe A and B. The pressure difference of this two is to be
measured by multiple tube manometer. Oil with specific gravity 0.88 is in the upper
portion of inverted U-tube and mercury of specific gravity 13.6 in the bottom of
both end bends. Determine the pressure difference.
5. A pipe connected with a tank (diameter 3 m) has an inclination of θ with the
horizontal and the diameter of the pipe is 20 cm. Determine the angle θ which will
give a deflection of 5 m in the pipe for a gauge pressure of 1 m water in the tank.
Liquid in the tank has a specific gravity of 0.88.
6. At the top of a mountain mercury-barometer reading is 56 cm and thermometer
reading is -50 C. while at the foot-hill the reading is 75.2 cm. Assuming dry
adiabatic condition determine the height of the mountain. R=287 joule/[kg(m) deg C
abs]
7. An empty cylindrical bucket with negligible thickness and weight is forced with its
open end first into water until its lower edge is 4m below the water level. If the
diameter and length of the bucket are 0.3m and 0.8m respectively and the trapped
water remains at const. temp. What would be the force required to hold the bucket in
that position atmospheric pressure being 1.03 N/cm2
Hydrostatic force on surface:
1. A vertical gate of 5 m height and 3 m wide closes a tunnel running full with water.
The pressure at the bottom of the gate is 195 kN/m2. Determine the total pressure on
the gate and position of the centre of the pressure
2. A rectangular block of 4m x 2m is hinged at a point 0.25 m below the CG of the gate.
If the total depth of water is 7 m what horizontal force must be applied at the bottom
to keep the gate closed?
3. A vertical gate of 2m x 2m rests with its top edge 1 m below the water level. Find the
depth of such a horizontal line that a) the force on the top half is equal to the pressure
on the bottom half. b) The moments of the force at both half about the line are equal.
4. An opening in the dam is covered with a plate of 1 m square and is hinged on the top
and inclined at 600 to the horizontal. If the top edge of the gate is 2 m below the
water level what is the force required to open the gate by pulling a chain set at 450
angle with the plate and set to the lower end of the plate. The plate weights 2200 N.
5. A vertical gate of height H and width B held water to its one side up to the top level.
If the plate is divided by N such lines that the total pressure on each plate is equal
then show that the height of the each portion is given by h=H√(r/N) and the depth
of centre of pressure. of each portion is given by hp=(2/3)H[r 3/2- (r-1) 3/2]/ √N
6. A gate closing an opening is triangular in section and 1 m long. It is hinged on the
top and freely supported at one of the bottom ends as shown in the figure. If the gate
weights 25 kN/m3 find the height of the water that will automatically open the gate.
7. What would be the height of water level h when the gate will automatically tip?
8. What would be the height of water level h when the gate will automatically tip?
9. The length of a tainter gate is 1m perpendicular to the plane of the paper. Find out
the total horizontal force on the gate and the total water pressure on the gate.
10. A solid cylinder of 2.4 m diameter and 2.5 kN weight rests on the bottom of a tank
which is one meter long. Water and oil (specific gravity 0.75) are poured into the two
sides of the cylinder up to a depth of 0.6m and 1.2 m respectively. Find the
magnitude of vertical component of the force that keeps the cylinder touching the
tank bottom.
11. A gate as shown in the fig is hinged at O and it is in the form of a quadrant of a circle
of radius 1m. It supports water at one side. If the length of gate is 3.5m find the force
required to hold the gate.
12. A quarter circle (10 m diameter) gate which is 10 m wide perpendicular to the paper
holds water as shown in the figure. Find the force required to hold the gate. The
weight of the gate can be neglected.
13. Determine the total hydrostatic force on the curved surface as shown in the figure.
The width of the curved portion is 2 m perpendicular to the paper.
14. The hemispherical dome as shown in the figure weights 25 kN and holds water. The
dome is fixed to the floor by 3 bolts equally spaced. Find
Buoyancy:
1. A wooden cylinder of length L and diameter L/2 is floating on water with its axis
vertical. Locate the metacentre if the specific gravity of wood is 0.6
2. A wooden cylinder of length L and diameter D is to be floated in stable equilibrium
on a liquid keeping its axis vertical. What should be the relation between L and D if
the specific gravity of liquid and that of the wood are 0.6 and 0.8 respectively?
3. A hollow cylinder of outside diameter 1.5 m and length of 3.8 m and specific weight
75 kN per cubic meter floats just in stable equilibrium condition. Find the thickness
of the cylinder if the sea water has a specific weight of 10 kN per cubic meter.
4. A cone is floating in water with its apex vertically downward has a vertical height H
diameter D. If the specific gravity of the material is S then find the condition for
stable equilibrium.
5. To find the metacentre of a ship of 10,000 tonnes displacement a weight of 55
tonnes is placed at a distance of 6 m from the longitudinal centre plane to cause a
heel through an angle of 30. What is the metacentre height? Hence find the angle of
heel and its direction when the ship ahead and 2.8 MW is being transmitted by a
single propeller shaft @90 rpm.
6. A log of wood of 0.36 m x 0.36m cross section with specific gravity 0.8 floats in
water. Now if one of its edges is depressed to cause the log roll, find the period of
roll.
7. A float valve controlling the flow of a liquid of specific gravity 0.88 in a tank. The
spherical float has the diameter of 15cm and it is connected with a valve through a
weightless link ‘AOB’ mounted at the hinge O. length of the link AO is 0.2m and
that of OB is 0.5m. The oil flow stops when the free surface of liquid is 0.35 m
below the hinge. Now if the valve is to be pressed by a force of 10 N what should be
the weight of the float? The angle AOB is given as 1200 and the link AO should be
vertical when the flow is to be stopped.
Liquid in relative equilibrium:
1. An open rectangular open tank 6m x 4.5m x 3m high containing water up
to a level of 2m is accelerated at 3m/ s2 A)horizontally along the longer side. B)
vertically downwards and C) vertically upwards D) in 300 inclination with
horizontal along the longer side. Find in each case the shape of the free water
surface and the pressure on the bottom and on the side walls.
2. An open cylindrical container 0.5m in diameter and 0.8m in height ,filled with oil
upto 0.5 m and rotating about its vertical axis. Find the speed at which the liquid will
start to spill over and also the speed at which the point of the bottom centre will just
exposed. The specific gravity of liquid is 0.88.
3. An upright manometer of limbs 1m high and 0.5 m apart are filled with water upto
0.5 m. now if it starts rotating about a vertical axis 0.2m apart from one limb @ 10
rad/s what would be the levels of liquid in the two limbs.
4. A conical vessel with the base open is filled completely with water and is rotated at
60 rpm. If only 0.0142 m3 of water is left then calculate the ratio of radius and
height of the cone.
5. An open tank of 5 m length contains upto a depth of 2m of oil of specific gravity
0.8. Now if the tank accelerates along a 300 inclined plane keeping the bottom of the
tank horizontal at 3.5 m/s2 what would be the shape of free water surface? Also find
the pressure intensity at the bottom, front and rear side of the tank.
Fluid kinematics:
1. Calculate thee change of velocity for a water flow which flows through a pipe of 0.2
m diameter and enters to a pipe of 0.1 m diameter. The water flows at a rate of 2200
litre per hour.
2. What will be the change of velocity of water through a nozzle of diameter 0.01m if a
change of flow takes place from 1500 lph to 1200 lph?
3. The velocity components are in the following cases find the third component to
satisfy the continuity equation. a) U=x3 +2y2 +z3 and V= -x2y – yz - xy. b) U= log
(y2 + z2) and W= log (x2 + y2).
4. The velocity field of a fluid is given by V=10x2yi + 20yzj - 4xyk +25tk. Find the
acceleration of the fluid at a point (2, 3, -2) at a time t= 0.5. Also identify the local
and convective component.
5. An incompressible fluid flows past a solid plate. If the x component of the flow is
given by U= x2y2 + 2xy obtain the velocity field and also the acceleration at point
(2, 2).
6. The velocity field of an incompressible fluid is given by V = 3y2i - 8xj. Verify
whether the fluid is in motion. If so, determine the expression for stream function
and the direction of the stream line through (1, 2).
7. Derive the equation of stream function and velocity potential for a uniform flow of
stream of velocity 5m/s at a angle of 300 to the x-axis in a two dimensional field.
8. The x- component of the velocity for a two dimensional fluid flow over a plate is
given by U= 3y – y2 .where y is measured from the surface in a perpendicular
direction. Verify if the flow is rotational. If so find the rotational velocity at (3, 2).
9. For a given two dimensional flow is v = -4y. Determine the algebraic expression for
velocity field and stream function. If the flow is irrotational find the pressure
gradient at point (2, 3). What is the direction of streamline through this point, the x-y
plane being horizontal?
10. For a two dimensional flow stream function is given as 5(y2-x3). Find out the
velocity components and the discharge passing between the streamlines through the
point (3,2) and (4,2)