Chapter 11-12: Fluid Mechanics
1) Density
A plastic block of dimensions 0.02 m x 0.03 m x 0.04 m has a mass of 0.03 kg. What is the density? A) 800 kg/m³ B) 1600 kg/m³ C) 1250 kg/m³ D) 1200 kg/m³
2) Pressure. Pascal principle. Hydraulic press
The weight of a car is 13000 N. The car is placed on a piston of a hydraulic press with radius 0.125 m. What force needs to be applied to the smaller piston of radius 0.05 m to lift the car? A) 5200 N B) 3600 N C) 4830 N D) 2080 N
3) Pressure variation with depth
What is the pressure at a depth of 15 m below the sea surface. The density of seawater is 1030 kg/m³. A) 1.01 x 10⁵ N/m² B) 1.51 x 10⁵ N/m² C) 2.52 x 10⁵ N/m² D) 2.48 x 10⁵ N/m²
4) Apparent weight and buoyant force
The weight of a metal box is 40 N. The apparent weight of the box fully submerged in water is 30 N. What is the buoyant force of water? A) 70 N B) 40 N C) 10 N D) 30 N
5) Buoyant force. Archimedes' principle
A 4-kg iron cylinder is supported by a string while submerged in water. The density of iron is 7860 kg/m³. What is the tension in the string? A) 2.5 N B) 23.7 N C) 19.6 N D) 34.2 N
6) Buoyant force. Floating condition
The object floats in water with 80% of its volume below the surface. What is the density of the object? The density of water is 1000 kg/m³. A) 1005 kg/m³ B) 800 kg/m³ C) 1250 kg/m³ D) 700 kg/m³
7) Archimedes' principle
An object floats with half of its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the weight of the object? A) 4000 N B) 2000 N C) 1000 N D) 500 N
8) A tip of an iceberg
What percentage of the volume of an iceberg is beneath the surface of the water? The density of ice is 917 kg/m³. The density of seawater is 1030 kg/m³. A) 76% B) 25% C) 89% D) 50%
9) Continuity equation
Water flows through a cylindrical pipe. The radius of the wider section of the pipe is 0.02 m. The velocity of water in the wider section of the pipe is 1 m/s. The radius of the narrower part is 0.01 m. What is the velocity of water in the narrower part? A) 0.5 m/s B) 4 m/s C) 2 m/s D) 0.25 m/s
10) Bernoulli's equation. Horizontal flow
Water flows through a cylindrical pipe. The radius of the narrow section is R₁ and the radius of the wider section is R₂=2R₁. The velocity of water in the narrow section is 12 m/s; the pressure in the narrow section is 30000 N/m². What is the pressure in the wider section? A) 74000 N/m² B) 97500 N/m² C) 30000 N/m² D) 49000 N/m²
11) Bernoulli's equation. Vertical flow
A hole of radius 0.001 m occurs in the bottom of a water storage tank at a depth of 15 m. What is the velocity water flowing through the hole. (Assume that the pressure of water on top of the tank and in the hole is equal to the atmospheric pressure, and the velocity of water in the tank is much slower than the velocity of water in the hole.) A) 17.1 m/s B) 24.3 m/s C) 31 m/s D) 43 m/s