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 N-s/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.
10. The space between discs of a viscous clutch is filled with an oil of viscosity μ. Develop the algebraic expression for the power and torque transmitted in terms of input and output rpm Wi and Wo and the disc radius and disc spacing as ‘R’ and ‘a’ respectively.
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.
6. Two thin flat plates tilted at an angle α are placed in a liquid of known surface tension Y and contact angle θ as shown in the figure. At the free surface of the liquid the plates are at a distance ‘L’ apart and have width ‘b’ into the page. The liquid rises a height ‘h’ between the plates .Determine the total upward force acting on the liquid column and hence determine the expression of surface tension in terms of the other variables.
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 pressure on the top half is equal to the pressure on the bottom half. b) The moments of the pressure 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. Calculate the total pressure and the centre of pressure for the right angular triangular plane immersed in water with the horizontal arm parallel to the free water surface and 5 m below the surface. The triangle has the vertical and horizontal arm 3 m each.
6. 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
7. 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.
8. What would be the height of water level h when the gate will automatically tip?
9. What would be the height of water level h when the gate will automatically tip?
10. 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.
11. 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.
12. 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.
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. 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).