the continuity equation a fundamental principle in fluid dynamics expresses the conservation of

HESI A2

HESI A2 Physics

1. In fluid dynamics, the continuity equation, a fundamental principle, expresses the conservation of:

A. Momentum
B. Mass
C. Energy
D. Angular momentum

Correct answer: B

Rationale: The continuity equation in fluid dynamics is a statement of the conservation of mass, making choice B the correct answer. It states that the mass entering a system must equal the mass leaving the system, assuming no mass is created or destroyed within the system. Conservation of momentum (choice A) is related to Newton's laws of motion and is not directly expressed by the continuity equation. Conservation of energy (choice C) involves different principles like the first law of thermodynamics and is not the focus of the continuity equation. Angular momentum (choice D) is also a different concept related to rotational motion and not described by the continuity equation.

2. Enthalpy (H) is a thermodynamic property defined as the sum of a system's internal energy (U) and the product of its pressure (P) and volume (V). The relationship between these is:

A. H = U + PV
B. H = U - PV
C. H = U / PV
D. H = PV / U

Correct answer: A

Rationale: Enthalpy (H) is defined as H = U + PV, where U represents internal energy, P is pressure, and V is volume. Enthalpy includes both the internal energy of a system and the energy required to create space for the system against an external pressure. Therefore, the correct relationship between enthalpy, internal energy, pressure, and volume is H = U + PV. Choice B is incorrect as subtracting PV would not account for the work done against pressure. Choice C is incorrect as dividing U by PV doesn't represent the definition of enthalpy. Choice D is incorrect as dividing PV by U is not the correct relationship based on the definition of enthalpy.

3. In an adiabatic process, there is:

A. No heat transfer (Q = 0) between the system and the surroundings.
B. Isothermal compression or expansion (constant temperature).
C. Constant pressure throughout the process (isobaric process).
D. No change in the system's internal energy (energy is conserved according to the first law).

Correct answer: A

Rationale: In an adiabatic process, choice A is correct because adiabatic processes involve no heat transfer between the system and its surroundings (Q = 0). This lack of heat transfer is a defining characteristic of adiabatic processes. Choices B, C, and D do not accurately describe an adiabatic process. Choice B refers to an isothermal process where temperature remains constant, not adiabatic. Choice C describes an isobaric process with constant pressure, not specific to adiabatic processes. Choice D mentions the conservation of energy but does not directly relate to the absence of heat transfer in adiabatic processes.

4. What is the kinetic energy of a 500-kg wagon moving at 10 m/s?

A. 50 J
B. 250 J
C. 2.5 × 10^4 J
D. 5.0 × 10^5 J

Correct answer: C

Rationale: The formula for calculating kinetic energy is KE = 0.5 × mass × velocity². Given the mass of the wagon is 500 kg and the velocity is 10 m/s, we can substitute these values into the formula: KE = 0.5 × 500 kg × (10 m/s)² = 0.5 × 500 kg × 100 m²/s² = 25,000 J or 2.5 × 10⁴ J. Therefore, the kinetic energy of the 500-kg wagon moving at 10 m/s is 2.5 × 10⁴ J. Choice A (50 J) is incorrect because it is too low; Choice B (250 J) is incorrect as it does not match the correct calculation; Choice D (5.0 × 10^5 J) is incorrect as it is too high. The correct answer is C (2.5 × 10^4 J).

5. A 10-kg object moving at 5 m/s has an impulse acted on it causing the velocity to change to 15 m/s. What was the impulse that was applied to the object?

A. 10 kg⋅m/s
B. 15 kg⋅m/s
C. 20 kg⋅m/s
D. 100 kg⋅m/s

Correct answer: D

Rationale: Impulse is the change in momentum of an object. The initial momentum is calculated as 10 kg × 5 m/s = 50 kg⋅m/s, and the final momentum is 10 kg × 15 m/s = 150 kg⋅m/s. The change in momentum (impulse) is 150 kg⋅m/s - 50 kg⋅m/s = 100 kg⋅m/s. Therefore, the impulse applied to the object is 100 kg⋅m/s. Choices A, B, and C are incorrect because they do not reflect the correct calculation of the impulse based on the change in momentum of the object.