#1. A viscometer measures the torque required to rotate a cylinder (radius 50 mm, length 100 mm) at 60 rpm inside a stationary cylinder (radius 52 mm). If the torque is 0.8 N·m, what is the fluid viscosity?
#2. An oil film between two parallel plates (area 0.2 m², gap 0.5 mm) requires 150 N force to move one plate at 0.3 m/s. What is the dynamic viscosity?
#3. Water (ρ = 1000 kg/m³, K = 2.2 GPa) in a pipe experiences a pressure surge of 5 MPa. What is the percentage change in density?
#4. A soap bubble has inner and outer radii of 25 mm and 25.1 mm. If surface tension is 0.03 N/m, what is the pressure difference between inside and outside?
#5. For a non-Newtonian power-law fluid with τ = K(du/dy)ⁿ where K = 0.5 Pa·sⁿ and n = 0.7, find the shear stress at a shear rate of 100 s⁻¹.
#6. A falling-sphere viscometer uses a 3 mm diameter steel ball (ρ = 7850 kg/m³) in oil (ρ = 890 kg/m³). Terminal velocity is 15 mm/s. Calculate oil viscosity.
#7. A capillary viscometer tube (L = 50 cm, D = 1 mm) has a throughflow of 0.5 mL/min under a pressure drop of 8 kPa. What is the fluid viscosity?
#8. An air bubble (D = 2 mm) rises through water (σ = 0.073 N/m). What excess pressure exists inside the bubble?
#9. A thin film of oil (μ = 0.4 Pa·s) separates a 100 mm diameter piston from a cylinder. The radial clearance is 0.05 mm and piston length is 150 mm. What force is needed to move the piston at 2 m/s?
#10. The isothermal compressibility of a liquid is 5 × 10⁻¹⁰ Pa⁻¹. A 10 m³ volume of this liquid is subjected to a 30 MPa pressure increase. What is the volume reduction?
#11. A triangular gate (base 3 m at top, height 4 m pointing down) is submerged with its base at the water surface. Find the hydrostatic force on the gate.
#12. A conical plug (base D = 0.3 m, height 0.4 m) seals a tank opening. Water pressure on the base is 80 kPa. Ignoring atmospheric pressure on the outer surface, what force holds the plug in place?
#13. A curved surface is defined by y = x² (0 ≤ x ≤ 2 m) submerged vertically with x horizontal. The width is 3 m. Calculate the horizontal component of hydrostatic force.
#14. A tank accelerates horizontally at 3 m/s². It contains water 2 m deep and 4 m long. What is the maximum depth of water during acceleration?
#15. A cylindrical container (D = 0.5 m, partially filled with water to depth 0.3 m) rotates about its vertical axis. At what angular velocity will water just reach the rim if the container height is 0.4 m?
#16. A ship’s hull has a waterplane area of 1500 m² and displaces 8000 tonnes of seawater (ρ = 1025 kg/m³). Calculate the metacentric height if BM = 4.5 m and KG = 6.2 m, with KB = 3.8 m.
#17. A rectangular caisson (8 m × 4 m × 6 m tall) is ballasted to float with 4 m submerged in seawater. Find the metacentric height for rolling about the longer axis.
#18. A submerged gate (2 m × 3 m) is hinged at its bottom edge, which is 6 m below the water surface. What horizontal force at the top edge is needed to just open the gate?
#19. A spherical tank (D = 3 m) is half filled with oil (SG = 0.85). Calculate the horizontal force on one half of the tank (vertical plane through center).
#20. An iceberg (ρ = 917 kg/m³) floats in seawater (ρ = 1025 kg/m³). What fraction of the iceberg volume is above water?
#21. A dam face is parabolic: y = 0.1x² where y is horizontal depth and x is vertical height from base. Width is 20 m, height is 10 m. Calculate horizontal hydrostatic force.
#22. A barge (20 m × 8 m) floats in freshwater with draft 2 m. A 50-tonne crane is placed at the center. What is the new draft?
#23. A vertical rectangular gate (2 m wide, 3 m tall) has water on both sides: 4 m deep on one side, 1.5 m deep on the other. Find net hydrostatic force.
#24. A tank of water rotates at 100 rpm about its vertical axis. What is the pressure difference between a point on the axis and a point 0.3 m from the axis at the same elevation?
#25. A floating hydrometer (mass 20 g, stem D = 5 mm) floats with 4 cm of stem above liquid surface in water. In an unknown liquid, 6 cm is exposed. What is the unknown liquid density?
#26. A Venturi meter (D₁ = 150 mm, D₂ = 75 mm, Cd = 0.98) measures water flow. If manometer shows 350 mm Hg difference, what is the flow rate?
#27. Water flows through a siphon from tank A (elevation 12 m) to tank B (elevation 3 m). The siphon rises to 15 m. If losses = 2.5 m, what is exit velocity?
#28. A pump (η = 75%) lifts 50 L/s of water 30 m through a pipe with head loss 8 m. Inlet and outlet velocities are 2 m/s and 8 m/s respectively. What power is required?
#29. An orifice (D = 40 mm, Cd = 0.62, Cv = 0.98) discharges water under 5 m head. Calculate the discharge and actual exit velocity.
#30. A horizontal pipe has a leak. Upstream: D = 100 mm, P = 400 kPa, V = 3 m/s. Downstream: D = 100 mm, V = 2.5 m/s. What volume flow rate is lost through the leak?
#31. Water flows in a 100 mm pipe at 4 m/s. A 50 mm nozzle is attached. Neglecting losses, what is the power in the jet?
#32. A turbine operates between two reservoirs (elevation difference 80 m). Penstock: D = 1 m, L = 500 m, f = 0.02, Q = 5 m³/s. If turbine η = 90%, find power output.
#33. Water issues from a tank as a horizontal jet 2 m below the surface. The jet lands 4 m horizontally from the tank. What is the coefficient of velocity?
#34. A Pitot tube in a water pipe shows stagnation pressure of 180 kPa. A wall tap at the same location shows 150 kPa. What is the flow velocity?
#35. A conical tank (base D = 2 m, apex at bottom) drains through a 50 mm orifice (Cd = 0.6). Initial depth is 3 m. How long to drain completely?
#36. Water at 8 m/s enters a diffuser (D₁ = 100 mm, D₂ = 200 mm, η = 85% pressure recovery). What is the static pressure rise?
#37. A fire pump delivers water through 100 m of 75 mm hose (f = 0.025) and a 20 mm nozzle at 12 L/s. What pump head is required?
#38. Two tanks (surface elevations 25 m and 10 m) are connected by a pipe (D = 150 mm, L = 200 m, f = 0.02). A pump (η = 70%) in the line adds 20 m head. Find flow rate.
#39. A jet pump entrains secondary flow. Primary: 5 L/s at 40 m/s. Combined exit: 15 L/s. What is the exit velocity assuming no losses and mixing occurs at constant area?
#40. Water flows over a broad-crested weir (width 5 m) with upstream head 0.6 m. Using Q = 1.6×L×H^1.5, calculate the discharge.
#41. Three pipes in parallel connect reservoirs A and B (ΔH = 20 m). Pipe 1: D = 100 mm, L = 100 m; Pipe 2: D = 150 mm, L = 200 m; Pipe 3: D = 200 mm, L = 150 m. All have f = 0.02. Find total flow.
#42. A pipe network has pipes AB (L=1000m, D=300mm), BC (L=800m, D=250mm), and AC (L=1200m, D=200mm) forming a triangle. Flow enters at A (100 L/s) and exits at B (40 L/s) and C (60 L/s). Using Hardy-Cross, estimate flow in AB.
#43. A pump with curve H = 60 – 800Q² (H in m, Q in m³/s) feeds a system H_sys = 15 + 200Q². What is the operating point flow rate?
#44. Two identical pumps (H = 50 – 1000Q² each) operate in series on a system H = 10 + 500Q². Find the combined operating flow rate.
#45. Two identical pumps (H = 40 – 800Q² each) operate in parallel on a system H = 20 + 400Q². Find total flow rate.
#46. A pipe (D = 250 mm, L = 3 km, f = 0.02, ε = 0.15 mm) carries water from reservoir (elev. 100 m) to town (elev. 30 m). What flow rate is delivered?
#47. Water flows through a sudden contraction (D₁ = 300 mm to D₂ = 150 mm) at Q = 80 L/s. Using K = 0.42 for this geometry, find the head loss.
#48. A pipeline (D = 200 mm) has three 90° bends (K = 0.3 each), a gate valve (K = 0.15), and entrance/exit losses. Total L = 500 m, f = 0.018. For Q = 60 L/s, find total head loss.
#49. An aging pipe’s roughness has increased from 0.046 mm to 0.3 mm. For D = 150 mm and Re = 200,000, by what factor has the friction factor increased?
#50. A looped water distribution system has demands at nodes B (30 L/s), C (40 L/s), D (20 L/s). Supply enters at node A. Pipe AB: 500m × 200mm, BC: 400m × 150mm, CD: 300m × 150mm, DA: 600m × 200mm. Estimate pressure drop A to C.
#51. A pipe system has a high point where P = -50 kPa gauge. To avoid cavitation in water at 25°C (Pv = 3.17 kPa), what minimum absolute pressure is needed?
#52. For economic pipe sizing, the optimum diameter balances pipe cost and pumping cost. If pumping cost ∝ D⁻⁵ and pipe cost ∝ D, what diameter ratio minimizes total cost compared to doubling flow?
#53. A pipe (D = 100 mm, L = 50 m) delivers water from a constant-head tank. If the pipe is replaced with two parallel pipes of equal diameter to double the flow, what diameter is needed for each new pipe (same total head loss)?
#54. A water main (D = 300 mm, f = 0.015) serves three branches at 200 m, 400 m, and 600 m from the source. Each branch draws 20 L/s. Main inflow pressure is 500 kPa. Find pressure at the last branch.
#55. The NPSH available at a pump is 8 m. If flow increases by 50%, by what factor does NPSH required typically increase (NPSH_R ∝ Q²)?
#56. A centrifugal pump (1450 rpm, 250 mm impeller) has Q = 40 L/s, H = 25 m. Calculate specific speed and identify pump type.
#57. A pump with 300 mm impeller at 1750 rpm produces 50 m head at 100 L/s. If impeller is trimmed to 270 mm, estimate new head and flow.
#58. A Francis turbine (N = 300 rpm) operates under H = 120 m producing 25 MW. Calculate specific speed and verify turbine selection.
#59. A Kaplan turbine has runner diameter 4 m and hub ratio 0.4. At 150 rpm under 20 m head with η = 93%, estimate power output.
#60. A Pelton wheel (D = 2 m, n = 300 rpm) receives a jet (d = 150 mm) at 100 m/s. With bucket angle 165° and η = 88%, find power.
#61. A pump has characteristics Q (L/s): 0, 20, 40, 60; H (m): 30, 28, 22, 12. Plot system curve H = 5 + 0.005Q² and find operating point.
#62. A fan delivers 3 m³/s at 1200 Pa total pressure when running at 1450 rpm with 5 kW shaft power. What are flow, pressure, and power at 1200 rpm?
#63. A compressor (inlet: 100 kPa, 300 K) has pressure ratio 6 and isentropic efficiency 82%. Find actual outlet temperature for air (k = 1.4).
#64. A hydraulic turbine has draft tube (inlet D = 2 m, V = 8 m/s; outlet D = 3 m, 3 m below). If losses = 0.5 m, what is pressure at draft tube inlet?
#65. Two pumps with curves H₁ = 40 – 500Q² and H₂ = 35 – 400Q² operate in parallel. Find combined curve equation.
#66. A pump cavitates when σ = NPSH/H drops below 0.08. If the pump operates at H = 50 m, what minimum NPSH is required?
#67. A gas turbine (m = 50 kg/s air, T₁ = 1400 K, P₁ = 1200 kPa, P₂ = 100 kPa) has isentropic efficiency 88%. Find power output (cp = 1.1 kJ/kg·K, k = 1.35).
#68. A Pelton turbine bucket velocity is optimum at U/V_jet = 0.46. For a jet velocity of 85 m/s, what is the optimal bucket peripheral velocity?
#69. An axial flow pump (D = 0.5 m, hub ratio 0.5) runs at 1000 rpm. Flow velocity is 4 m/s. Calculate flow rate.
#70. A reaction turbine has degree of reaction R = 0.6. If total head is 100 m, how much head is converted in the runner vs. guide vanes?
#71. Air (P₀ = 500 kPa, T₀ = 400 K) expands isentropically through a nozzle to Mach 2.5. Find exit temperature and pressure.
#72. A normal shock occurs in air flow at Mach 2.5, T₁ = 250 K, P₁ = 50 kPa. Find conditions after the shock.
#73. A converging-diverging nozzle has throat area 20 cm² and exit area 40 cm². For air from a reservoir at 600 kPa, 400 K, find mass flow rate when choked.
#74. A supersonic diffuser decelerates air from Mach 2.0 to Mach 0.5. If inlet static pressure is 30 kPa, what is exit static pressure assuming isentropic flow?
#75. Air at Mach 1.8 passes through an oblique shock with wave angle 40°. Find the deflection angle using oblique shock relations.
#76. A ramjet operates at Mach 3, altitude where P = 26 kPa, T = 220 K. Air decelerates to Mach 0.3 before combustion. Find temperature rise due to deceleration.
#77. A rocket nozzle expands gas from 3 MPa, 2500 K to exit pressure 10 kPa. Find exit Mach number assuming k = 1.25.
#78. Fanno flow (adiabatic with friction) in a duct starts at Mach 0.3. If fL*/D = 5.3 at inlet, what is the Mach number at duct exit if actual fL/D = 3?
#79. Rayleigh flow (frictionless with heat addition) starts at Mach 0.5. If q = 300 kJ/kg is added (cp = 1005 J/kg·K), find exit Mach number for initially T₀ = 400 K.
#80. A blowdown wind tunnel has reservoir at 1 MPa, 300 K. The test section operates at Mach 2.0. How long can it run if tank volume is 10 m³ and mass flow is 5 kg/s?
#81. A pitot tube in supersonic flow reads P₀₂ = 150 kPa. Static pressure is 30 kPa. Estimate free stream Mach number accounting for bow shock.
#82. Air in a constant-area duct (D = 50 mm, L = 2 m, f = 0.005) enters at Mach 0.2, P = 200 kPa, T = 350 K. Find exit Mach number.
#83. An over-expanded nozzle has design exit Mach 2.5 but operates with back pressure causing exit shock. If P_exit/P_back = 0.7, estimate actual exit Mach.
#84. A scramjet combustor receives air at Mach 2.5, 1000 K, 50 kPa. Heat addition of 600 kJ/kg occurs. Estimate exit Mach and temperature.
#85. A shock tube has driver section at 10 atm, test section at 1 atm, both air at 300 K. Estimate incident shock Mach number.
#86. A flat plate (L = 2 m, W = 1 m) has laminar flow to x = 0.5 m, then turbulent. At 30 m/s in air (ν = 1.5 × 10⁻⁵ m²/s), find total drag using appropriate correlations.
#87. The displacement thickness at x = 1 m on a flat plate with U∞ = 20 m/s in air (ν = 1.5 × 10⁻⁵ m²/s) is (laminar):
#88. A cylinder (D = 50 mm, L = 1 m) in crossflow at Re = 10⁵ has CD = 1.2. At 15 m/s in water (ρ = 1000 kg/m³), find drag force.
#89. Airflow separation on a sphere occurs at approximately 82° from the stagnation point at low Re. At Re = 10⁶, separation moves to about 120° due to:
#90. A NACA 0012 airfoil at 8° angle of attack has CL = 0.85 and CD = 0.012. For a wing (span 12 m, chord 1.5 m) at 80 m/s in air (ρ = 1.1 kg/m³), find L/D.
#91. The momentum thickness θ of a turbulent boundary layer on a flat plate varies as θ/x = 0.036/Re_x^0.2. At x = 3 m with U = 25 m/s in air (ν = 1.5 × 10⁻⁵ m²/s), find θ.
#92. A sphere (D = 0.1 m, ρ_s = 2500 kg/m³) is released in oil (ρ = 900 kg/m³, μ = 0.8 Pa·s). Find time to reach 90% of terminal velocity.
#93. A streamlined body has form drag coefficient 0.04 and skin friction coefficient 0.006. At 50 m/s, frontal area 0.8 m², wetted area 4 m² in air (ρ = 1.2 kg/m³), find total drag.
#94. An aircraft wing (area 30 m², AR = 8) has CL = 0.6 at cruise. Using lifting line theory, CD_i = CL²/(π×AR×e) with e = 0.9, find induced drag at 250 m/s in air (ρ = 0.4 kg/m³).
#95. Vortex shedding from a cylinder at Re = 10⁴ has Strouhal number St = 0.21. For D = 0.05 m in a 10 m/s flow, find shedding frequency.
#96. A pump model (1:5 scale) tested at 1800 rpm delivers 20 L/s at 8 m head. The prototype runs at 600 rpm. Find prototype Q and H.
#97. A spillway model (1:36 scale) passes 0.5 m³/s. If Froude similitude applies, what prototype discharge corresponds to this?
#98. A propeller (D = 3 m, N = 200 rpm) in water (ρ = 1000 kg/m³) produces 50 kN thrust. A 1:10 model is tested in a wind tunnel (ρ = 1.2 kg/m³) at the same advance ratio. Find model thrust.
#99. For a dam spillway, both Froude and Reynolds similarity cannot be simultaneously satisfied. A 1:25 model is tested using Froude similarity. If model Re = 2 × 10⁵, what is prototype Re?
#100. A wind tunnel model of a building (1:100 scale) experiences 15 N wind load at 30 m/s. What load would the prototype experience at 15 m/s wind?
