Q1. Bernoulli's theorem is based on conservation of:

Mass
Momentum
Energy
Angular momentum

Difficulty: Easy · Topic: Bernoulli's Theorem

Solution

Bernoulli's equation is derived from the work-energy theorem and represents conservation of energy in fluid flow.

Q2. Surface tension of a liquid is measured in SI units as:

N/m
N·m
Pa
N/m²

Difficulty: Easy · Topic: Surface Tension

Solution

Surface tension = Force per unit length = N/m.

Q3. The pressure at the bottom of a lake of depth 20 m is (density of water = 10³ kg/m³, g = 10 m/s², P_atm = 10⁵ Pa):

3 × 10⁵ Pa
2 × 10⁵ Pa
1 × 10⁵ Pa
4 × 10⁵ Pa

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³ × 10 × 20 = 10⁵ + 2×10⁵ = 3×10⁵ Pa.

Q4. The terminal velocity of a sphere falling through a viscous liquid is proportional to:

Radius
Radius²
1/Radius
1/Radius²

Difficulty: Easy-Medium · Topic: Viscosity

Solution

From Stokes' law: v_t = 2r²(ρ-σ)g/(9η). So v_t ∝ r².

Q5. The pressure at depth 5 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

2.5 atm
1.5 atm
3.0 atm
1.0 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×5 = 150000 Pa = 1.5 atm.

Q6. The pressure at depth 10 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

4.0 atm
2.0 atm
3.0 atm
1.5 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×10 = 200000 Pa = 2.0 atm.

Q7. The pressure at depth 15 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

3.5 atm
2.5 atm
2.0 atm
5.0 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×15 = 250000 Pa = 2.5 atm.

Q8. The pressure at depth 25 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

3.0 atm
7.0 atm
3.5 atm
4.5 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×25 = 350000 Pa = 3.5 atm.

Q9. The pressure at depth 30 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

3.5 atm
4.0 atm
5.0 atm
8.0 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×30 = 400000 Pa = 4.0 atm.

Q10. The pressure at depth 40 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

6.0 atm
4.5 atm
10.0 atm
5.0 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×40 = 500000 Pa = 5.0 atm.

Q11. The pressure at depth 50 m in water is (g=10 m/s², P_atm=10⁵ Pa, ρ=10³ kg/m³):

12.0 atm
6.0 atm
5.5 atm
7.0 atm

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P = P_atm + ρgh = 10⁵ + 10³×10×50 = 600000 Pa = 6.0 atm.

Q12. Water flows through a pipe of area 10 cm² at 2 m/s. If the pipe narrows to 5 cm², the velocity is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂. v₂ = 10×2/5 = 4 m/s.

Q13. Water flows through a pipe of area 5 cm² at 4 m/s. If the pipe narrows to 2 cm², the velocity is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂. v₂ = 5×4/2 = 10 m/s.

Q14. Water flows through a pipe of area 20 cm² at 1 m/s. If the pipe narrows to 10 cm², the velocity is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂. v₂ = 20×1/10 = 2 m/s.

Q15. Water flows through a pipe of area 4 cm² at 5 m/s. If the pipe narrows to 2 cm², the velocity is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂. v₂ = 4×5/2 = 10 m/s.

Q16. Water flows through a pipe of area 8 cm² at 3 m/s. If the pipe narrows to 4 cm², the velocity is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂. v₂ = 8×3/4 = 6 m/s.

Q17. A fluid flows through a pipe. At section 1: area 10 cm², velocity 2 m/s. At section 2: area 5 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q18. A fluid flows through a pipe. At section 1: area 12 cm², velocity 3 m/s. At section 2: area 6 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q19. A fluid flows through a pipe. At section 1: area 14 cm², velocity 4 m/s. At section 2: area 7 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q20. A fluid flows through a pipe. At section 1: area 16 cm², velocity 5 m/s. At section 2: area 8 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q21. A fluid flows through a pipe. At section 1: area 18 cm², velocity 6 m/s. At section 2: area 9 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q22. A fluid flows through a pipe. At section 1: area 20 cm², velocity 7 m/s. At section 2: area 10 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q23. A fluid flows through a pipe. At section 1: area 22 cm², velocity 8 m/s. At section 2: area 11 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q24. A fluid flows through a pipe. At section 1: area 24 cm², velocity 9 m/s. At section 2: area 12 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q25. A fluid flows through a pipe. At section 1: area 26 cm², velocity 10 m/s. At section 2: area 13 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q26. A fluid flows through a pipe. At section 1: area 28 cm², velocity 11 m/s. At section 2: area 14 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q27. A fluid flows through a pipe. At section 1: area 30 cm², velocity 12 m/s. At section 2: area 15 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q28. A fluid flows through a pipe. At section 1: area 32 cm², velocity 13 m/s. At section 2: area 16 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q29. A fluid flows through a pipe. At section 1: area 34 cm², velocity 14 m/s. At section 2: area 17 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q30. A fluid flows through a pipe. At section 1: area 36 cm², velocity 15 m/s. At section 2: area 18 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q31. A fluid flows through a pipe. At section 1: area 38 cm², velocity 16 m/s. At section 2: area 19 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q32. A fluid flows through a pipe. At section 1: area 40 cm², velocity 17 m/s. At section 2: area 20 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q33. A fluid flows through a pipe. At section 1: area 42 cm², velocity 18 m/s. At section 2: area 21 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q34. A fluid flows through a pipe. At section 1: area 44 cm², velocity 19 m/s. At section 2: area 22 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q35. A fluid flows through a pipe. At section 1: area 46 cm², velocity 20 m/s. At section 2: area 23 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q36. A fluid flows through a pipe. At section 1: area 48 cm², velocity 21 m/s. At section 2: area 24 cm². Velocity at 2 is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

A₁v₁ = A₂v₂.

Q37. Pressure at depth 1m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+1/10=1.1 atm.

Q38. Pressure at depth 3m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+3/10=1.3 atm.

Q39. Pressure at depth 5m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+5/10=1.5 atm.

Q40. Pressure at depth 7m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+7/10=1.7 atm.

Q41. Pressure at depth 9m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+9/10=1.9 atm.

Q42. Pressure at depth 11m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+11/10=2.1 atm.

Q43. Pressure at depth 13m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+13/10=2.3 atm.

Q44. Pressure at depth 15m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+15/10=2.5 atm.

Q45. Pressure at depth 17m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+17/10=2.7 atm.

Q46. Pressure at depth 19m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+19/10=2.9 atm.

Q47. Pressure at depth 21m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+21/10=3.1 atm.

Q48. Pressure at depth 23m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+23/10=3.3 atm.

Q49. Pressure at depth 25m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+25/10=3.5 atm.

Q50. Pressure at depth 27m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+27/10=3.7 atm.

Q51. Pressure at depth 29m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+29/10=3.9 atm.

Q52. Pressure at depth 31m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+31/10=4.1 atm.

Q53. Pressure at depth 33m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+33/10=4.3 atm.

Q54. Pressure at depth 35m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+35/10=4.5 atm.

Q55. Pressure at depth 37m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+37/10=4.7 atm.

Q56. Pressure at depth 39m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+39/10=4.9 atm.

Q57. Pressure at depth 41m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+41/10=5.1 atm.

Q58. Pressure at depth 43m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+43/10=5.3 atm.

Q59. Pressure at depth 45m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+45/10=5.5 atm.

Q60. Pressure at depth 47m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+47/10=5.7 atm.

Q61. Pressure at depth 49m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+49/10=5.9 atm.

Q62. Pressure at depth 51m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+51/10=6.1 atm.

Q63. Pressure at depth 53m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+53/10=6.3 atm.

Q64. Pressure at depth 55m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+55/10=6.5 atm.

Q65. Pressure at depth 57m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+57/10=6.7 atm.

Q66. Pressure at depth 59m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+59/10=6.9 atm.

Q67. Pressure at depth 61m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+61/10=7.1 atm.

Q68. Pressure at depth 63m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+63/10=7.3 atm.

Q69. Pressure at depth 65m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+65/10=7.5 atm.

Q70. Pressure at depth 67m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+67/10=7.7 atm.

Q71. Pressure at depth 69m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+69/10=7.9 atm.

Q72. Pressure at depth 71m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+71/10=8.1 atm.

Q73. Pressure at depth 73m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+73/10=8.3 atm.

Q74. Pressure at depth 75m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+75/10=8.5 atm.

Q75. Pressure at depth 77m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+77/10=8.7 atm.

Q76. Pressure at depth 79m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+79/10=8.9 atm.

Q77. Pressure at depth 81m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+81/10=9.1 atm.

Q78. Pressure at depth 83m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+83/10=9.3 atm.

Q79. Pressure at depth 85m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+85/10=9.5 atm.

Q80. Pressure at depth 87m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+87/10=9.7 atm.

Q81. Pressure at depth 89m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+89/10=9.9 atm.

Q82. Pressure at depth 91m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+91/10=10.1 atm.

Q83. Pressure at depth 93m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+93/10=10.3 atm.

Q84. Pressure at depth 95m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+95/10=10.5 atm.

Q85. Pressure at depth 97m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+97/10=10.7 atm.

Q86. Pressure at depth 99m in water (atm):

Difficulty: Easy-Medium · Topic: Fluid Pressure

Solution

P=1+ρgh/P0=1+99/10=10.9 atm.

Q87. Pipe: A1=2cm², v1=1m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*1/1=2 m/s.

Q88. Pipe: A1=2cm², v1=2m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*2/1=4 m/s.

Q89. Pipe: A1=2cm², v1=3m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*3/1=6 m/s.

Q90. Pipe: A1=2cm², v1=4m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*4/1=8 m/s.

Q91. Pipe: A1=2cm², v1=5m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*5/1=10 m/s.

Q92. Pipe: A1=2cm², v1=6m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*6/1=12 m/s.

Q93. Pipe: A1=2cm², v1=7m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*7/1=14 m/s.

Q94. Pipe: A1=2cm², v1=8m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*8/1=16 m/s.

Q95. Pipe: A1=2cm², v1=9m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=2*9/1=18 m/s.

Q96. Pipe: A1=4cm², v1=1m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*1/1=4 m/s.

Q97. Pipe: A1=4cm², v1=1m/s, A2=2cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*1/2=2 m/s.

Q98. Pipe: A1=4cm², v1=2m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*2/1=8 m/s.

Q99. Pipe: A1=4cm², v1=2m/s, A2=2cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*2/2=4 m/s.

Q100. Pipe: A1=4cm², v1=3m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*3/1=12 m/s.

Q101. Pipe: A1=4cm², v1=3m/s, A2=2cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*3/2=6 m/s.

Q102. Pipe: A1=4cm², v1=3m/s, A2=3cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*3/3=4 m/s.

Q103. Pipe: A1=4cm², v1=4m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*4/1=16 m/s.

Q104. Pipe: A1=4cm², v1=4m/s, A2=2cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*4/2=8 m/s.

Q105. Pipe: A1=4cm², v1=5m/s, A2=1cm². v2=

Difficulty: Easy-Medium · Topic: Continuity

Solution

v2=A1v1/A2=4*5/1=20 m/s.

Chapter 10: Mechanical Properties of Fluids

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