Conservation of Mass in Fluid Mechanics: Master Mass Balance

Question 1

Which of the following is a direct application of the conservation of mass principle?

Accepted Answer

Determining the mass flow rate of a fluid through a nozzle

Answer

Calculating the velocity of a fluid flowing through a pipe

Answer

Predicting the pressure drop in a fluid flowing through a pipe

Answer

Analyzing the flow of a fluid around an airfoil

Question 2

In a closed system, the total mass contained within the system changes over time.

Accepted Answer

False

Answer

True

Question 3

The mass conservation equation can be used to determine the mass flow rate through an aircraft engine.

Accepted Answer

True

Answer

False

Question 4

Which of the following is NOT a common application of the conservation of mass equation in engineering?

Accepted Answer

Design of bridges

Answer

Design of chemical reactors

Answer

Design of aircraft wings

Answer

Design of water distribution networks

Question 5

Which assumption is NOT made when deriving the conservation of mass equation?

Accepted Answer

Fluid properties are uniform throughout the flow region.

Answer

Mass within a moving fluid volume remains constant.

Answer

Mass entering a control volume equals mass leaving.

Answer

Mass of fluid in any given volume is conserved.

Question 6

Provide a clear definition of mass flow rate and explain its significance in fluid mechanics.

Accepted Answer

Mass flow rate represents the rate at which mass flows through a given cross-sectional area.

Answer

Mass flow rate refers to the total mass of fluid present in a system.

Answer

Mass flow rate measures the rate of change in fluid velocity.

Question 7

Which of the following is the correct form of the continuity equation for an incompressible fluid?

Accepted Answer

∂ρ/∂t + ∇·(ρu) = 0

Answer

ρu·∇ρ = 0

Answer

ρ∂u/∂t + u·∇ρ = 0

Answer

∂u/∂t + ∇·(ρu) = 0

Question 8

In a steady, incompressible flow, the divergence of the velocity field is:

Accepted Answer

Zero

Answer

Non-zero

Answer

Constant

Answer

Proportional to the fluid density

Question 9

In mass conservation problems, which boundary conditions are commonly used?

Accepted Answer

Both inflow and outflow conditions

Answer

No-slip condition

Answer

Inflow condition

Answer

Outflow condition

Question 10

Which statement accurately describes the principle of mass conservation in fluid flow?

Accepted Answer

Mass entering a region equals mass leaving the region

Answer

Mass entering a region is greater than mass leaving

Answer

Mass leaving a region is greater than mass entering

Answer

Mass in a closed system remains constant

Question 11

Define the continuity equation.

Accepted Answer

A mathematical expression representing the conservation of mass

Answer

A formula for calculating fluid velocity

Answer

A method for measuring fluid mass flow rate

Answer

A graphical representation of the flow field

Question 12

Which of the following statements expresses the fundamental principle of mass conservation for an incompressible fluid?

Accepted Answer

Mass entering a system equals mass leaving the system

Answer

Density remains constant throughout the fluid flow

Answer

Velocity remains constant throughout the fluid flow

Answer

Pressure drop is proportional to the flow rate

Question 13

What is the significance of the continuity equation in fluid mechanics?

Accepted Answer

Relates mass flow rate to fluid properties and geometrical parameters

Answer

Describes pressure gradients within a fluid

Answer

Predicts the direction of fluid flow

Answer

Determines the viscosity of a fluid

Question 14

How does mass flow rate relate to fluid density?

Accepted Answer

Mass flow rate is directly proportional to density

Answer

Mass flow rate is inversely proportional to density

Answer

Mass flow rate is independent of density

Answer

Mass flow rate is exponentially proportional to density

Question 15

Consider steady, incompressible fluid flow through a pipe. Which of the following equations represents the principle of mass conservation in this context?

Accepted Answer

ρA₁u₁ = ρA₂u₂

Answer

ρ₁V₁ = ρ₂V₂

Answer

m₁ = m₂

Answer

Q = Av

Question 16

When fluid flows through a nozzle, the flow area decreases. What happens to the fluid velocity as a result?

Accepted Answer

Increases

Answer

Decreases

Answer

Remains constant

Answer

May vary depending on fluid properties

Question 17

What is the key significance of the continuity equation in fluid mechanics?

Accepted Answer

It ensures the conservation of mass in flow systems.

Answer

It provides a relationship between velocity and pressure.

Answer

It helps determine the efficiency of fluid machines.

Answer

It simplifies the analysis of complex flow phenomena.

Question 18

In a pipe, how does an increase in fluid density affect the mass flow rate?

Accepted Answer

Increases

Answer

Decreases

Answer

Remains constant

Answer

May vary depending on pipe diameter

Question 19

Which of the following is NOT a common method for measuring mass flow rate?

Accepted Answer

Thermometer

Answer

Venturi meter

Answer

Orifice plate

Answer

Ultrasonic flowmeter

Question 20

What is the primary purpose of using control volumes in the analysis of fluid flow problems?

Accepted Answer

To apply the conservation laws

Answer

To simplify complex flow patterns

Answer

To determine the pressure distribution

Answer

To calculate the flow resistance