JH ACADEMY 1. 1 | Page 2. The velocity distribution of a fluid over a plate is given by u= where u is the velocity along the plate, in m/sec at a distance of y m above the plate. Find the shear stress at y= 0.1m. The dynamic viscosity of the fluid is 8.3×N.S/ 3. Vertical semi circular area of radius ‘r’ is submerged in a liquid with its diameter at the liquid surface, find the depth of centre of pressure. 4. A body of volume 0.15 nedded a force of 300 N to keep it submerged in water. How much force would be needed to submerge it in another liquid of RD = 0.932? 5. A jet of water 150 mm in diameter moving at 25 m/s strikes a plate at rest. Find the force exerted normal to the plate when a) Plate is held normal to the jet b) The plate makes to the jet 6. If in a two dimensional flow over a solid plate, the velocity potential is ∅, obtain a) Velocity, passing through the point (2,3) b) Acceleration at a point (2,3) 7. Calculate the capillary effect in mm in a glass tube of 3mm diameter, when immersed in mercury. The value of the surface tension of mercury at C in contact with air is 0.51 N/m. contact angle for mercury = 8. If the equation of velocity profile over a flat plate is where is the velocity profile over a flat plate is distance in m, determine shear stress at y = 75 mm. Take μ = 8.35 poise. 9. As shown in fig. pipe M contains carbon tera chloride of specific gravity 1.594 under a pressure of 1.05 bars and pipe N contains oil of specific gravity 0.8. If the pressure in the pipe N is 1.75 bar and the Manometric fluid is mercury, find the difference x between the levels of mercury? 10. An orifice meter with orifice diameter 10 cm is inserted in a pipe of 20 cm diameter. The pressure gauges fitted u/s and d/s of the orifice meter give readings of 19.62 N/ and the discharge of water through the pipe? 11. 12. Fuel is pumped up in a 30 cm diameter and 15 Km long pipe at the rate of 750 kg/min. The pipe is laid at an upgrade of 1:300. The specific gravity of 13. fuel is 0.95 and its kinematic viscosity 20 stokes. Find the power required to pump oil? 14. The stream function for a 2.D flow is given by calculate the velocity at a point p(4,5). Find also the velocity potential function? 15. If for a 2-D potential flow, the velocity potential is given by Ø=4x(3y-4), determine the velocity at the point (2,3), Determine also the value of stream function at the point (2,3)? 16. A horizontal venturimeter with inlet diameter 20cm and throat diameter 10cm is used to measure the flow of water. The pressure at the inlet is 17.658 and the vacuum pressure at the throat is 30cm of mercury. Find the discharge of water through the venturimeter. Total =0.98? 17. An oil of viscosity 0.1 and relative density 0.9 is through a circular pipe of diameter 50mm and length 300m. The rate of flow of fluid through the pipe is 3.5. Find the pressure drop in a length of 300m and also shear stress at the pipe wall? 18. The stream function is given by . Determine the magnitude of velocity components at the point (2, 1). 19. For laminar flow of an oil having dynamic viscosity μ= 1.766 poise in a 0.3m diameter pipe, the velocity distribution is parabolic with a maximum point velocity of 3 m/s at the centre of the pipe. Calculate the shearing stress at the pipe wall and within the fluid 50 mm from the pipe wall? 20. A rectangular channel 4 m wide discharges 16 cumecs of water, if the specific energy head is 2.25 m; find the possible depth of flow. 21. A channel has vertical wall 1.2 m apart and a semi circular invert. If the centre line depth is 0.9 m and the bed slope is 0.37 m per km, find the value of c in Chezy’s formula if the discharge is 0.54 cumecs 22. A spillway 7.2 m high and 150 m long discharges 2150 /s under a head of 4 m. if a 1:16 model of the spillway is to be constructed, find the model dimensions, head over the model and the model discharge. 23. An oil of specific gravity 0.85 and viscosity 5CP flows through a pipe of diameter 400 mm at the of 50 lit/sec. find the head lost in friction in this pipe of length 100 km. assume that f= where is Reynolds number. 24. A jet of water of 75 mm diameter strikes a curved vane at its centre with a velocity of 20 m/sec. the curved vane is moving with a velocity of 5 m/s in the direction of jet. Find the force exerted on the plate in the direction of the jet, power and efficiency of jet. Assume the plate to be smooth. 25. A jet of water 50 mm in diameter issues with a velocity of 10 m/sec and impinges normally on a stationary flat plate which moves in forward motion. Find the force exerted on the plate and work done. 26. Find the equation of stream line passing through (2, 2) for the fluid flow 27. 20 cm diameter jet of oil of specific gravity 0.85 strikes a stationary flat plate at an angle of to the normal. Estimate the force exerted on the plate when the velocity of the jet is 25 m/sec 28. An oil of relative density 0.9 flows through a vertical pipe of diameter 20 cm. the flow is measured by a 20 cm×10 cm venturimeter. The throat is 30 cm above the inlet section. A differential U-tube manometer containing mercury is connected to the throat and the inlet. If co-efficient of discharge is 0.99. What is the Manometric reading for a flow of 50 lit/sec? 29. A conical pipe has diameters 0.4 m and 0.8 m at its two ends. The smaller end is 2 m above the larger end. For a flow of 0.3 /sec of water, the pressure at lower end is 10 KPa. Assuming a head loss of 2 m estimate the pressure at the smaller end. 30. A soap bubble 50 mm diameter has an internal pressure in excess of the outside pressure of 25 N/. Calculate tension in the soap film? 31. The diameter of pipe at the section 1 and 2 are 15 cm and 20 cm respectively. Find the discharge through the pipe if velocity of water at section the 1 is 4 m/s. determine also the velocity at section at section 2. 32. Calculate the rate of flow of water through a pipe of diameter 300 mm, when the difference of pressure head between the two ends of a pipe 400 m apart is 5 m of water. Take value as f = 0.009 33. Find the stream function velocity at a point P (2,3) for a 2-D fluid flow, velocity potential is 34. A wooden block of sp.gr.0.75 floats in water. If the size of the block is 1 m×0.5 m ×0.4 m, find its Meta centre height for a roll on its longitudinal axis. 35. In an experiment on V-notch the flow is connected in a vertical cylinder tank 0.9 m diameter. It is found that the depth of water in the tank increases by 0.65 m in 16.8s. determine the coefficient of discharge of the notch? 36. A body weighing 450 N with a flat surface area of 0.023 slides down lubricated inclined plane making a angle with the horizontal. For viscosity of 0.1 N.S/ and body speed of 3 m/s, determine the lubricant film thickness? 37. Find the pressure represented by a column of (i) 10 cm of water (ii) 5 cm of oil of relative density 0.75 (iii) 2 cm of mercury 38. Find the absolute pressure at a depth of 5 m below the surface of a liquid of relative density 0.85. the barometer reading on the surface is 750 mm of mercury. A 6 m deep tank contains 4 m water and 2 m of soil of relative density 0.88. Determine the pressure at bottom of the tank. 39. Determine the pressure difference between points and B for the set up shown in fig. 40. For the manometer shown in fig. calculate the pressure difference between points M and N. 41. A Kaplan turbine develops 1500 Kw power at a head of 30m and operates at a speed of 40 s rpm. Find the specific speed of turbine 42. A circular channel 1.2m in diameter is laid on a slope of 0.008. The manning’s for the channel can be as 0.018. calculate the specific energy when the depth of flow is 0.6 m. 43. A rectangular channel 1.5 m wide carries a discharge of 9.0 / sec at a depth of 2.0 m calculate the specific energy and the depth alternate to the given depth 2.0 m 44. A rectangular channel 2.0 m wide carries a discharge of 6.0 /s. if the specific energy is 1.8 m. calculates the alternate depths? 45. In a rectangular channel 2.0m wide to two alternate depths to a given specific energy are 0.3 m and 1.2 m respectively. Calculate the discharge? 46. In a rectangular channel, the alternate depths are 1.0 m and 2.0 m respectively. The specific energy head in m is? 47. The Froude number of flow in rectangular channel is 0.73. if the depth of flow is 1.5m, the specific energy in meters is? 48. Super critical flow at Froude number =2.0 occurs at a depth of 0.63 m in rectangular channel.tje critical depth is? 49. What is the maximum discharge that may be carried by a 3.2 m wide rectangular channel at a specific energy of 1.8 m? 50. What is the lowest possible specific energy for a water discharge of 12 to flow through a 3.0 m wide rectangular channel? 51. Wide at 100 blows along a long flat surface 50m long. Estimate (i) the thickness of boundary layer at distances of 5m and 50m from the leading edge and (ii) shear stress at 5m and 50m from the leading edge 52. Air flows over a flat plate 1m long at a velocity of 6. Determine a) the boundary layer thickness at end of plate b).share stress at the middle of the plate c). Total drag per unit length on the sides of the plate. P=1.226 , ϑ=0.15* ? 53. What is the pressure within a droplet of water 0.05 mm diameter, if the pressure outside the droplet is 10.3 m of water σ=0.075? 54. An annular plate 3m external diameter and 1.5 m internal diameter is immersed in water with its greatest and least depths below water surface as 3.6m and 1.2m respectively. Determine the total pressure and the position of the centre of pressure on the face of the plate.? 55. A rectangular weir is 2m long and has a head of 0.675m. Find the discharge taking into account two and contractions =0.6? 56. A cylinder has a diameter 0.3m and specific gravity of 0.75. What is the maximum permissible length in order that it may float in water its axis vertical? 57. An iceberg weighing 8976 floats in the ocean with a volume of 600 above the surface. Determine the total volume of the iceberg if specific weight of ocean water is 10055 ? 58. In a steady flow two points A and B are 0.5 m apart cn a straight streamline. If the velocity of flow varies linearly between A and B what is the acceleration at each point if the velocity at A is and the velocity at B is 6? 59. A compound piping system consists of 1800m of 0.5m, 1200 m of 0.4 m and 600 m of 0.3 new cast iron pipes connected in series. Convert the system to (a) an equivalent length of 0.4m pipe and equivalent size pipe 3600m long. ? 60. A tank 1.5m high on a trolley and is full of water. It has an orifice of diameter 0.1 at 0.3 m from the bottom of the tank. If the orifice is suddenly opened, what will be the propelling force on the trolley? =0.6. 61. A small glass sphere of specific gravity 2.65 has a diameter of 3mm. If the sphere falls 0.6m in 30sec. through a liquid of specific gravity 0.85. What is the absolute rituality of the liquid? 62. A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4H: 3V. The bed slope is 0.002. The channel is lined with smooth concrete (manning’s n=0.0012). the hydraulic radius in m for a depth of flow of 3.0 m is ? 63. Water flows with flow rate of 0.3 through a pipe AB of 10m length and of uniform. The end B is above end A and the pipe makes an angle of 3 to the horizontal. For a pressure of 12 at the end B, the corresponding pressure at the end A is? 64. Water flows through a 100mm diameter pipe with a velocity of 0.015. if the kinematic viscosity o water is 1.13*, the friction factored of the pipe material is? 65. A river reaches of 2km long with maximum flood discharge of 10000 to be physically modeled in the lab where maximum available discharge is 0.2. For a geometrically similar model based on equality of Froude number, the length of river reach (m) in the model is? 66. The flow of water (mass density = 1000, kinematic viscosity = ) in a commercial pipe yields an average shears stress at the pipe boundary =600 . The thickness of laminar sub layer is? 67. Water emerges from an agee spill way with velocity=13.72 and from depth=0.3m at its toe. The tail water depth required to form a hydraulic jump at the toe as? 68. The velocity in at a point in a 2.0 flow is given as V=2i+3J. The equation of stream line polling through the point is? 69. A stream function is given by φ=2y+(x+1). The flow rate across a line joining points A(3,0) and B(0,2) is? 70. The velocity field for flow is given by V= (5x+6y+7z)j +(3x+2y=7z)k and the density varies as p=. in order that mass is conserved, the value of λ should be? 71. Flow rate fluid (density =1000 ) in a small diameter tube is 800 . the length and the diameter of the tube are 2m and 0.5 mm respectively the pressure drop in 2m length is equal to 2.0 mpa. The viscosity of fluid is 72. Am open cylindrical vessel of 20cm diameter and 50cm high contain at 180 rpm about its access calculate the pressures on the bottom at the centre and at the edge of the vessel? 73. For the following flow find the equation of the streamline passing through ? 74. An unsteady velocity field is given by u=+3y ϑ=4t+5x. Calculate the acceleration at the point (5,3) at time t=2. 75. Consider the velocity field given by u= , ϑ=2xy. Find the circulation around an area bounded by (1,1),(2,1) and 1,2 ? 76. Determine the components of rotation for u=xz ϑ=- w=y - 77. A liquid undergone a change of pressure from 6.87mpa to 13.73 mpa to make the volumetric change of elasticity of liquid? 78. Water is flowing through pipe having inlet and exit diameter of 25cm respectively. If the velocity of water at inlet section is 5 find the velocity head at exit and also rate of discharge 79. In a hydraulic jump taking place in a horizontal rectangular channel the sequent depths are 0.3m and 1.5m respectively jump in a horizontal rectangular channel is 0.22. The sequent depth ratio of the jump is? 80. The Froude number of a subcritical stream at the end a hydraulic jump in horizontal rectangular channel is 0.22. The sequent depth ratio of the jump is? 81. Water is flowing pipe having inlet and exit diameter of 25cm and 12cm respectively. If the velocity of water at inlet section is 5find the velocity head at exit and also rate of discharge? 82. Determine the number of the impellers required for a multistage pump to lift 4200 against a total head of 185 m at a speed of 750rpm. The specific speed is to exceed 700? 83. At what height from water surface a centrifugal pump may be installed in the following case to avoid cavitations. At mos pheric pressure 101 kpa, vapour pressure 2.34 kpa. Inlet and other losses in section pipe 1.55m, effective head of pump 52.5m and cavitations parameter σ=0.118? 84. Determine the specific speed of turbine working under a head of 30m and developing 2000 km. the speed of runner is 553.2 rpm? 85. A jet of water issues from a sharp edged vertical orifice under a constant head of 0.51m. at a certain point of issuing set, the horizontal and vertical co-ordinates measured from the vena-contract are 0.406 m and 0-085m respectively, Determine . if =0.62 find ? 86. The difference in the water surface levels of two reservoirs which are connected by a siphon is 8m. The length of the siphon is 600m and its diameter o.3m. Assuming f=0.02 determine the discharge when the siphon is running fall? 87. The percentage error in the computed discharge over a triangular notch corresponding to an error of 1% in the measurement of head over the notch would be? 88. At a rated capacity of 44 cumecs, a centrifugal pump develops 36m of head when operating at 1459 rpm. Its specific speed is? 89. A hydraulic jump occurs in a wide rectangular channel with initial and sequent depths of 0.5m and 2.0m respectively. Calculate (a). the discharge (b) possible critical depth (c) the energy loss? 90. A trapezoidal channel with bottom width of 3m and side slope of 1v:1.5h carries a discharge of 8.0 with the flow depth of 1.5m.the Froude number of the flow is? 91. Oil flows through a 200 mm diameter horizontal cast iron pipe, (friction factor f=0.0225) of length 500m. the volumetric flow rate is 0.2 . The head loss in m due to friction is (Assure g-9.81 )? 92. An incompressible fluid flows over a flat plate with zero pressure gradients. The boundary layer thickness 1mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by factor 4 then, the boundary layer thickness at the same location in mm will be? 93. Water at c is flowing through a 1.0 km long G.I. pipe of 200mm diameter at the rate of 0.07. if value of Darcy friction factor for this pipe is 0.02 and density of water 1000, the pumping power in (kw) required to maintain the flow is? 94. A venturimeter of 20mm throat diameter is used to measure the velocity of water in a horizontal pipe of 40mm diameter. If the pressure difference between the pipe and throat section is found to be 30ka then, neglecting frictional losses, the flow velocity is? 95. An incompressible fluid (kinematic viscosity, 7.4*, specific gravity 0.88) is hold between two parallel plates if the top plate is moved with a velocity of 0.5 x while bottom one is held stationary then fluid attains a linear plates. The shear stress on the surface of top plate is? 96. A franeis turbine running at 200 rpm develops a power of 5000 kw under a head of 25m. Determine the power output under a head of 100m? 97. A francis turbine working under a head of 5m at a speed of 210 rpm develops 75kw when the rate of flow of water is 1.8. The runner diameter is 1m. if the head on this turbine is increased to 16m, determine its new speed, discharge & power? 98. The Reynolds number for flow of a certain fluid in a circular tube is specified as 2500. What will be the Reynolds nuber when the tube diameter is increased by 20% and the fluid velocity is decreased by 40% keeping fluid same? 99. The velocity components in the x and y directions are given by u=λx-y ϑ=x-.The value of for a possible field involving an incompressible fluid is? 100. A hydraulic turbine develops 1000 kw power for a head of 40m. if the head is reduced to 20m, the power developed is? 101. Velocity vector of a flow field is given as v=2xyi-zjthe vortices vector at (1,1,1)is? 102. The cross, section of an open channel consists of semi: - circular bottom 1.2m in diameter and with vertical sides. If the depth of water is 1.2m and the bed slope is 1 in 2500, calculate the discharge. Take Chezy’s c as 65