Computational Fluid Dynamics Multiple Choice Questions on “Incompressible Flows – Pressure Calculation”.
1. Which of these is a disadvantage of the Navier-Stokes equations?
a) No independent-equation for pressure
b) No independent-equation for temperature
c) No equation to find the density
d) No equation to find the velocity
Answer: a
Clarification: The Navier-stokes equations do not have a separate equation to find the pressure values at different points. Pressure gradients are present in different momentum equations making it a dependent form.
2. Which of these statements is true for an incompressible flow?
a) Absolute mass flux is not important
b) Absolute density is not important
c) Absolute temperature is not important
d) Absolute pressure is not important
Answer: d
Clarification: There is no need for the absolute value of pressure in an incompressible flow. This is because the flow is not affected by this value. But, their gradients in all the directions are important as it will affect the flow.
3. How is pressure calculated in a compressible flow?
a) Pressure correction equation
b) Equation of state
c) Momentum equation
d) Energy equation
Answer: b
Clarification: In the compressible flows, the density terms of the continuity equation do not cancel out. So, density can be determined using the continuity equation. Using this density value and the equation of state, we can get the pressure values.
4. Which of these equations are used to get the pressure values in the incompressible flows?
a) Continuity and momentum equations
b) Momentum and energy equations
c) Energy equation and equation of state
d) Equation of state and continuity equations
Answer: a
Clarification: The divergence of the momentum equation is taken. The equation obtained from this is then simplified using the continuity equation to get the pressure values. So, a combination of continuity and momentum equations is needed here.
5. The pressure equation for the incompressible equation is _________
a) Eulerian equation
b) Divergence equation
c) Lagrangian equation
d) Poisson equation
Answer: d
Clarification: The resultant equation obtained by modifying the existing governing equations to get the pressure values is a Poisson equation for pressure. A Poisson equation is a partial differential equation of elliptic type.
6. Which of these terms in the pressure equation become zero?
a) Viscous and pressure terms
b) Viscous and transient terms
c) Pressure and source terms
d) Source and transient terms
Answer: b
Clarification: The viscous terms in the pressure equation are cancelled because of constant viscosity. The transient terms are cancelled out as the density is constant. These cancellations are made by implementing the continuity equation.
7. The pressure equation in the incompressible flows contain _________
a) Taylor series terms
b) Hermitian operator
c) Laplacian operator
d) Fourier series terms
Answer: c
Clarification: The Poisson’s equation which is formulated for finding the pressure values has a Laplace operator. This is the product of the divergence operator in the continuity equation and the gradient operator in the momentum equation.
8. According to the explicit time-advanced method for getting pressure, which of these is correct?
a) Continuity is enforced at the previous step after starting to solve the current step
b) Momentum conservation is enforced at the previous step after starting to solve the current step
c) Momentum equation is enforced at each step before moving to the next step
d) Continuity is enforced before at each step moving to the next step