Engineering Questions with Answers - Multiple Choice Questions

Computational Fluid Dynamics – Continuity Equation – Finite Control Volume

1 - Question

The physical principle behind the continuity equation is __________
a) Mass conservation
b) Zeroth law of thermodynamics
c) First law of thermodynamics
d) Energy conservation
Explanation: Continuity equation is derived from the mass conservation principle. It states that for an isolated system, the mass of the system must remain constant.

2 - Question

Which of these models directly gives this equation?
tvρdV+sρV⃗ .dS=0

a

b

c

d

Explanation: The equation is in conservative integral form. So, the model must be finite control volume fixed in space.

3 - Question

Which of these models directly gives this equation?
DDtvρdV=0
a)

b

c

d

Explanation: The equation is the non-conservative form of the integral continuity equation. This is obtained from a finite control volume moving along with the flow.

4 - Question

Consider a model of finite control volume (volume V and surface area S) fixed in space with elemental volume dV, vector elemental surface area dS⃗ , density ρ and flow velocity V⃗ . What is the net mass flow rate out of the surface area?
a) ∬VρV⃗ .dV
b) ρV⃗ .dS⃗
c) ∭VρV⃗ .dS⃗
d) ∬VρV⃗ .dS⃗
Explanation: In general, mass flow rate=density × velocity × area For this case, elemental mass flow rate = ρV⃗ .dS⃗ total mass flow rate=∬VρV⃗ .dS⃗

5 - Question

Consider a model of finite control volume (volume V and surface area) fixed in space with elemental volume dV, vector elemental surface area dS⃗ , density ρ and flow velocity V⃗ . What is the mass inside the control volume?
a) ∬sρV⃗ .dS⃗
b) ∭VρdV
c) ρdV
d) ∂∂t∭VρdV
Explanation: Mass=density × volume mass inside dV=ρdV mass inside V=∭VρdV.

6 - Question

Consider a model of finite control volume (volume V and surface area) moving along the flow with elemental volume dV, vector elemental surface area dS⃗ , density ρ and flow velocity V⃗ . What is the time rate of change of mass inside the control volume?
a) ∭VρdV
b) ∂∂t∭VρdV
c) DDt∭VρdV
d) ρdV
Explanation: Substantial derivative is used as the model is moving. mass=density × volume mass inside dV=ρdV mass inside V=∭VρdV time rate of change of mass inside DDt∭VρdV.

7 - Question

To convert the non-conservative integral equation of mass conservation into the conservative integral form, which of these theorems is used?
a) Stokes theorem
b) Kelvin-Stokes theorem
c) Gauss-Siedel theorem
d) Gauss Divergence Theorem
Explanation: The expansion of non-conservative integral equation gives two volume integral terms. One of these terms representing the mass flow is converted into surface integral using the Gauss Divergence theorem.

8 - Question

Consider a model of finite control volume (volume V and surface area) fixed in space with elemental volume dV, vector elemental surface area dS⃗ , density ρ and flow velocity V⃗ .
ρV⃗ .dS⃗ is positive when _____________
a) The mass flow is outward
b) The mass flow is inward
c) The mass flow is positive
d) The mass flow is negative
Explanation: dS⃗ always points outwards to the control volume. So, the product ρV⃗ .dS⃗ is positive when the mass flow is outwards.

9 - Question

What is the physical statement of mass conservation equation for a finite control volume fixed in space?
a) Net mass flow through the control surface = constant
b) Rate of change of mass inside the control volume = constant
c) Net mass flow through the control surface = Rate of change of mass inside the control volume
d) Net mass flow through the control surface≠Rate of change of mass inside the control volume
Explanation: Statement of mass conservation equation for a finite control volume fixed in space: Net mass flow through the control surface is equal to the rate of change of mass inside the control volume.

10 - Question

What is the physical statement of mass conservation equation for a finite control volume moving along with the flow?
a) Rate of change of mass inside the control volume = 0
b) Rate of change of mass inside the control volume = constant
c) Net mass flow through the control surface = Rate of change of mass inside the control volume
d) Net mass flow through the control surface≠Rate of change of mass inside the control volume