#1. A hydraulic oil has a kinematic viscosity of 65 cSt and a density of 890 kg/m³. Determine the dynamic viscosity of the oil.
#2. Water at 20°C has a surface tension of 0.0728 N/m. A soap solution reduces the surface tension by 40%. What is the surface tension of the soap solution?
#3. A liquid has a bulk modulus of 2.1 GPa. If the pressure increases by 42 MPa, what is the percentage reduction in volume?
#4. The specific gravity of glycerin is 1.26. What is the density of glycerin in kg/m³?
#5. A fluid has a density of 850 kg/m³ and a dynamic viscosity of 0.025 Pa·s. Calculate the kinematic viscosity in m²/s.
#6. A capillary tube with an inner diameter of 1.5 mm is inserted into mercury (surface tension = 0.485 N/m, contact angle = 140°, density = 13,600 kg/m³). Calculate the capillary depression.
#7. The specific weight of a fluid is 8.5 kN/m³. What is its density?
#8. An oil droplet in water has a diameter of 3 mm. If the interfacial tension is 0.025 N/m, what is the pressure difference across the droplet interface?
#9. A fluid undergoes a 0.8% volume reduction when subjected to a pressure increase of 18 MPa. What is the bulk modulus of the fluid?
#10. The viscosity of an oil at 40°C is 0.15 Pa·s. If the density is 910 kg/m³, what is the kinematic viscosity in centistokes?
#11. A glass tube with an inner radius of 0.8 mm is inserted vertically into water (σ = 0.073 N/m, ρ = 998 kg/m³). Assuming perfect wetting, calculate the capillary rise.
#12. The speed of sound in a liquid is 1450 m/s and its density is 1025 kg/m³. What is the bulk modulus of the liquid?
#13. A Newtonian fluid flows between two parallel plates separated by 2 mm. If the shear stress is 25 Pa when the velocity gradient is 500 s⁻¹, what is the dynamic viscosity?
#14. Convert a kinematic viscosity of 0.0001 m²/s to Stokes.
#15. A fluid has a specific gravity of 0.85 and kinematic viscosity of 4 × 10⁻⁴ m²/s. What is its dynamic viscosity?
#16. A pressure gauge at the bottom of an open tank filled with oil (SG = 0.88) reads 65 kPa. What is the depth of oil in the tank?
#17. A U-tube manometer contains mercury (SG = 13.6). One end is open to atmosphere and the other is connected to a pressurized tank. If the mercury level difference is 35 cm, what is the gauge pressure in the tank?
#18. A rectangular gate 4 m wide and 3 m tall is submerged vertically with its top edge 2 m below the water surface. Calculate the hydrostatic force on the gate.
#19. A closed tank contains air at 50 kPa gauge above a 4 m layer of water. What is the absolute pressure at the bottom of the water? Assume atmospheric pressure is 101.3 kPa.
#20. A wooden cube (SG = 0.65) with a side length of 30 cm floats in water. What depth of the cube is submerged?
#21. A cylindrical buoy has a diameter of 1 m and length of 2 m. If it floats with 75% of its volume submerged in seawater (ρ = 1025 kg/m³), what is the mass of the buoy?
#22. An inclined manometer has a tube at 30° from horizontal. If the fluid (SG = 0.82) moves 15 cm along the tube, what is the pressure difference measured?
#23. A vertical circular gate with a diameter of 2 m has its center located 5 m below the water surface. Calculate the location of the center of pressure below the water surface.
#24. A tank contains three layers: 1.5 m of oil (SG = 0.85), 2.5 m of water, and 1 m of mercury (SG = 13.6). What is the gauge pressure at the bottom?
#25. A steel ball (ρ = 7800 kg/m³, diameter = 100 mm) is submerged in oil (ρ = 880 kg/m³). What is the apparent weight of the ball in the oil?
#26. A differential manometer connects two pipes A and B. The manometer fluid is carbon tetrachloride (SG = 1.59) and shows a difference of 25 cm. If pipe A is 30 cm higher than the reference level and pipe B is at the reference level, and both contain water, what is P_A – P_B?
#27. A hemispherical dome of radius 3 m covers an underwater structure. The center of the dome is 8 m below the water surface. Calculate the vertical component of the hydrostatic force on the dome.
#28. A rectangular pontoon 8 m × 4 m × 2 m floats in freshwater with a freeboard of 0.6 m. What is the mass of the pontoon?
#29. The atmospheric pressure at sea level is 101.3 kPa. At what depth in the ocean (ρ = 1025 kg/m³) does the absolute pressure reach 500 kPa?
#30. A trapezoidal gate has a top width of 2 m, bottom width of 4 m, and height of 3 m. It is submerged vertically with its top edge at the water surface. Calculate the hydrostatic force on the gate.
#31. Water flows through a pipe that expands from 80 mm to 120 mm diameter. If the velocity in the smaller section is 6 m/s, what is the velocity in the larger section?
#32. A rectangular duct 0.5 m × 0.3 m carries air at a velocity of 12 m/s. Calculate the volume flow rate.
#33. Crude oil (ρ = 870 kg/m³) flows through a pipeline at 0.025 m³/s. What is the mass flow rate?
#34. A pipe carrying water branches into two pipes. The main pipe has a diameter of 200 mm with velocity 3 m/s. One branch (100 mm diameter) carries 40% of the flow. What is the velocity in this branch?
#35. Air at standard conditions (ρ = 1.2 kg/m³) enters a compressor at 0.5 m³/s and exits at a density of 4.8 kg/m³. What is the exit volume flow rate if mass is conserved?
#36. Water flows at 15 L/s through a 75 mm diameter pipe. What is the average flow velocity?
#37. A fire hose with a 65 mm diameter nozzle discharges water at 25 m/s. What is the flow rate in liters per minute?
#38. An annular pipe has an outer diameter of 150 mm and inner diameter of 100 mm. If water flows at 2.5 m/s, calculate the volume flow rate.
#39. Natural gas (ρ = 0.72 kg/m³) flows through a 300 mm pipeline at 8 m/s. Calculate the mass flow rate.
#40. A circular pipe splits into 4 identical smaller pipes. If the main pipe has diameter D and velocity V, and the smaller pipes have diameter D/2, what is the velocity in each smaller pipe?
#41. Water flows from a large tank through a small orifice located 6 m below the water surface. What is the theoretical exit velocity?
#42. A horizontal pipe carrying water narrows from 150 mm to 75 mm diameter. At the larger section, the pressure is 400 kPa and velocity is 2 m/s. Find the pressure at the smaller section, neglecting losses.
#43. A pump increases the pressure of water flowing at 0.03 m³/s from 150 kPa to 450 kPa. If the pump efficiency is 80%, what power input is required?
#44. Water flows upward through a vertical pipe. At the lower section (diameter 100 mm), the pressure is 250 kPa and velocity is 4 m/s. At a point 8 m higher (diameter 150 mm), what is the pressure? Neglect losses.
#45. A Pitot-static tube measures an air stream. The stagnation pressure is 102.5 kPa and static pressure is 100 kPa. If air density is 1.18 kg/m³, what is the velocity?
#46. A siphon is used to drain water from a tank. The outlet is 3 m below the water surface and the highest point of the siphon is 1.5 m above the surface. What is the theoretical velocity at the outlet?
#47. Water flows through a Venturi meter with inlet diameter 100 mm and throat diameter 50 mm. If the pressure difference is 40 kPa, what is the flow rate? Assume ideal flow.
#48. A turbine extracts energy from water flowing at 2 m³/s. The inlet pressure is 500 kPa and outlet pressure is 100 kPa. If the turbine is 85% efficient, what is the power output?
#49. An inclined pipe carries water uphill with an elevation change of 15 m. If there is no velocity change and head losses are 3 m, what pressure increase must the pump provide?
#50. Water at 20 m/s enters a diffuser and exits at 5 m/s. What is the pressure rise across the diffuser, neglecting losses?
#51. A fire hydrant is connected to a water main at 350 kPa. When opened, water exits from a 50 mm nozzle. Assuming frictionless flow, what is the exit velocity?
#52. A horizontal water jet strikes a stationary vane and is deflected 60° from its original direction. If the jet velocity is 15 m/s and flow rate is 20 L/s, what horizontal force acts on the vane?
#53. Water flows from reservoir A (surface elevation 50 m) to reservoir B (surface elevation 20 m) through a pipe. If total head loss is 8 m, what is the velocity head at the pipe exit?
#54. A lawn sprinkler has 4 nozzles, each with 10 mm diameter. If water is supplied at 15 L/s total, what is the exit velocity from each nozzle?
#55. A submarine cruises at depth where gauge pressure is 600 kPa. A small hole develops. Assuming the interior is at atmospheric pressure, what is the initial velocity of water entering?
#56. Water (ν = 1.0 × 10⁻⁶ m²/s) flows at 2 m/s through a 25 mm diameter pipe. What is the Reynolds number?
#57. For laminar flow in a pipe with Reynolds number 1200, calculate the Darcy friction factor.
#58. Water flows at 3 m/s through a 50 mm diameter pipe that is 80 m long with f = 0.025. Calculate the head loss due to friction.
#59. A pipe system has the following minor losses: entrance (K=0.5), three 90° elbows (K=0.75 each), globe valve (K=10), and exit (K=1.0). If velocity is 3 m/s, what is the total minor head loss?
#60. A pipe has a diameter of 200 mm and absolute roughness of 0.3 mm. What is the relative roughness?
#61. Oil (μ = 0.08 Pa·s, ρ = 880 kg/m³) flows at 0.5 m/s through a 30 mm diameter horizontal pipe. Using Hagen-Poiseuille, find the pressure drop per meter of pipe.
#62. Using the Blasius correlation (f = 0.316/Re⁰·²⁵) for turbulent flow in a smooth pipe at Re = 80,000, calculate the friction factor.
#63. A sudden expansion from 50 mm to 100 mm pipe occurs. If the velocity in the smaller pipe is 6 m/s, what is the head loss?
#64. A ball valve with K = 0.05 is installed in a pipe where water flows at 4 m/s. What is the equivalent length of this valve if D = 100 mm and f = 0.02?
#65. Water flows through a 150 mm diameter pipe at a Reynolds number of 200,000. The pipe roughness is 0.15 mm. Using the Moody chart, estimate the friction factor.
#66. A horizontal pipeline (D = 80 mm, L = 200 m, f = 0.022) connects two tanks with a water level difference of 15 m. What is the flow velocity?
#67. A galvanized iron pipe (ε = 0.15 mm) has a diameter of 75 mm. In the fully rough turbulent regime, what is the friction factor?
#68. A pipe carrying water has a head loss of 12 m over 300 m length. If D = 100 mm, V = 2.5 m/s, what is the friction factor?
#69. A conical diffuser reduces velocity from 10 m/s to 4 m/s with a loss coefficient K = 0.2 (based on inlet velocity). What is the actual pressure rise if ρ = 1000 kg/m³?
#70. Two pipes in series have the same diameter. Pipe 1: L = 100 m, f = 0.02. Pipe 2: L = 150 m, f = 0.03. What is the equivalent length using f = 0.025?
#71. A commercial steel pipe (ε = 0.046 mm) has diameter 50 mm. At Re = 100,000, using the Colebrook equation, the friction factor is approximately:
#72. Water flows through a 90° miter bend (K = 1.1) at 5 m/s. What head loss occurs?
#73. A pipeline system has total minor loss coefficient ΣK = 8.5 and friction head loss of 12 m at a certain flow rate. If velocity is 3 m/s, what is the total head loss?
#74. A cast iron pipe (ε = 0.26 mm) with D = 100 mm operates in the transition zone at Re = 50,000. Estimate the friction factor.
#75. For a pipe with D = 200 mm, L = 500 m, and f = 0.018, what flow rate of water will result in a friction head loss of 10 m?
#76. A water jet (D = 75 mm, V = 30 m/s) strikes a stationary flat plate perpendicular to the flow. What force acts on the plate?
#77. Water flows through a 180° pipe bend at 0.15 m³/s. The pipe diameter is 150 mm and pressure is 250 kPa throughout. What force is required to hold the bend?
#78. A rocket engine expels 200 kg/s of exhaust gases at 2500 m/s relative to the rocket. What thrust is produced?
#79. A water jet (A = 0.005 m², V = 25 m/s) strikes a vane moving at 10 m/s in the same direction. What is the force on the vane?
#80. Water flows through a reducing elbow from 150 mm (P = 300 kPa) to 100 mm (P = 280 kPa) with a 60° turn. Flow rate is 0.05 m³/s. Find the force magnitude on the elbow.
#81. A fire monitor discharges 40 L/s of water through a 50 mm nozzle. What force must a firefighter exert to hold the nozzle steady?
#82. A jet of water (D = 60 mm, V = 20 m/s) is deflected 120° by a curved vane. Calculate the force on the vane.
#83. An aircraft jet engine has inlet velocity 200 m/s and outlet velocity 650 m/s with mass flow rate 80 kg/s. Fuel flow is negligible. What is the thrust?
#84. Water flows steadily through a horizontal pipe contraction. At section 1 (D = 200 mm): P = 400 kPa, V = 2 m/s. At section 2 (D = 100 mm): P = 370 kPa. What horizontal force holds the contraction?
#85. A pelton wheel bucket deflects a water jet (Q = 0.1 m³/s, V = 50 m/s) through 165°. What is the force on the bucket?
#86. A sphere (D = 200 mm) moves at 5 m/s through water (ρ = 1000 kg/m³). If the drag coefficient is 0.4, what is the drag force?
#87. An airfoil with a chord of 2 m and span of 10 m produces a lift coefficient of 1.4. At 60 m/s in air (ρ = 1.2 kg/m³), what is the lift force?
#88. A car has a frontal area of 2.2 m² and drag coefficient of 0.32. At 100 km/h in air (ρ = 1.2 kg/m³), what is the aerodynamic drag?
#89. A sphere (D = 5 mm) falls through glycerin (μ = 1.5 Pa·s, ρ = 1260 kg/m³) at terminal velocity. If sphere density is 2700 kg/m³, find terminal velocity using Stokes law.
#90. A flat plate (1 m × 0.5 m) is held perpendicular to a 20 m/s wind (ρ = 1.2 kg/m³). If CD = 1.2, what is the drag force?
#91. A cylinder (D = 0.3 m, L = 4 m) is perpendicular to a water flow at 3 m/s. If CD = 1.0, what is the drag force?
#92. A wind turbine blade element has a lift coefficient of 1.1 and drag coefficient of 0.08 at its operating condition. What is the lift-to-drag ratio?
#93. A parachutist (mass = 80 kg) falls at terminal velocity with a parachute having CD = 1.4 and diameter 8 m. In air (ρ = 1.1 kg/m³), what is terminal velocity?
#94. A submarine has wetted surface area of 2000 m² and skin friction coefficient of 0.003. At 10 m/s in seawater (ρ = 1025 kg/m³), what is the skin friction drag?
#95. A golf ball (D = 43 mm) travels at 60 m/s in air (ρ = 1.2 kg/m³). If the drag coefficient is 0.25, what is the drag force?
#96. Calculate the speed of sound in air at 15°C. (k = 1.4, R = 287 J/kg·K)
#97. An aircraft flies at 280 m/s through air at 260 K. What is the Mach number? (k = 1.4, R = 287 J/kg·K)
#98. Air flows at Mach 0.6 with static pressure 80 kPa. Using isentropic relations (k = 1.4), find the stagnation pressure.
#99. A supersonic wind tunnel operates at Mach 2.0. What is the Mach angle?
#100. Air (k = 1.4) flows isentropically at Mach 0.5 with stagnation temperature 400 K. What is the static temperature?
