Exploring Hydrodynamics and Pressure

Calculate the hydrostatic pressure at a depth of 10 meters in water, given that the density of water is approximately 1000 kg/m³ and the acceleration due to gravity is 9.81 m/s².

• 98100 Pa

• 50000 Pa

• 100000 Pa

• 98000 Pa

A fluid flows through a pipe with varying diameters. If the velocity of the fluid at the wider section of the pipe is 2 m/s and the diameter is 0.1 m, calculate the velocity of the fluid at the narrower section where the diameter is 0.05 m using Bernoulli's principle.

• The velocity at the narrower section is 4 m/s.

• The velocity at the narrower section is 8 m/s.

• The velocity at the narrower section is 2 m/s.

• The velocity at the narrower section cannot be determined without additional information.

A ship weighs 20,000 kg and is floating in water. If the density of water is 1000 kg/m³, calculate the volume of water displaced by the ship. Use Archimedes' principle to explain your calculation.

• The volume of water displaced is 20 m³, which is calculated by dividing the weight of the ship by the density of water (20,000 kg / 1000 kg/m³).

• The volume of water displaced is 10 m³, which is calculated by dividing the weight of the ship by the density of water (20,000 kg / 2000 kg/m³).

• The volume of water displaced is 25 m³, which is calculated by dividing the weight of the ship by the density of water (20,000 kg / 800 kg/m³).

• The volume of water displaced is 15 m³, which is calculated by dividing the weight of the ship by the density of water (20,000 kg / 1500 kg/m³).

A hydraulic system has a volume of 2 liters and a pressure of 1000 Pascals. If the volume is decreased to 1 liter, what will be the new pressure in the system assuming the relationship between pressure and volume is inversely related?

• The new pressure will be 500 Pascals.

• The new pressure will be 1000 Pascals.

• The new pressure will be 2000 Pascals.

• The new pressure will be 4000 Pascals.

A fluid with a viscosity of 0.8 Pa·s is flowing through a pipe with a diameter of 0.1 m. If the pressure drop across a 10 m length of the pipe is 2000 Pa, calculate the flow rate of the fluid using the Hagen-Poiseuille equation. What does this indicate about the fluid's resistance to flow?

• The flow rate is 0.002 m³/s, indicating low resistance to flow.

• The flow rate is 0.001 m³/s, indicating moderate resistance to flow.

• The flow rate is 0.0005 m³/s, indicating high resistance to flow.

• The flow rate is 0.003 m³/s, indicating very low resistance to flow.

If a small object with a weight of 0.1 N is placed on the surface of water, and the surface tension of the water is 0.072 N/m, what is the maximum diameter of the object that can float without sinking?

• 1.4 cm

• 2.0 cm

• 0.5 cm

• 3.0 cm

An object with a volume of 0.5 m³ is submerged in a fluid with a density of 1000 kg/m³. Calculate the buoyant force acting on the object. Assume the acceleration due to gravity is 9.81 m/s².

• 2455 N

• 4905 N

• 9810 N

• 14715 N

Given an airplane wing with a specific shape, calculate the pressure difference between the upper and lower surfaces of the wing using Bernoulli's equation. Assume the airspeed over the top of the wing is 70 m/s and the airspeed below the wing is 50 m/s. What is the pressure difference that contributes to lift?

• The pressure difference is calculated solely based on the weight of the aircraft.

• The pressure difference can be calculated using Bernoulli's equation, which relates the airspeed and pressure difference.

• The pressure difference is determined by the thrust generated by the wings.

• The pressure difference is zero if the wings are flat.

If a hydraulic system requires 50 liters of hydraulic fluid to operate efficiently and the fluid can transmit power at a rate of 5 kW per liter, what is the total power transmitted by the hydraulic fluid?

• 250 kW

• 200 kW

• 300 kW

• 150 kW

A fluid has a viscosity of 10 mPa·s at 20°C. If the temperature is increased to 60°C, and it is known that the viscosity decreases by 5% for every 10°C increase in temperature, what will be the new viscosity of the fluid at 60°C?

• 8.5 mPa·s

• 7.5 mPa·s

• 9.5 mPa·s

• 10.0 mPa·s