This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses 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
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: The divergence of the velocity field at the current step should be made zero. For this, the divergence of the velocity field at the previous step must be zero. So, continuity is zero at each step before moving to the next step.
9. The explicit method is preferred when __________
a) an accurate velocity field is needed
b) the pressure value is needed
c) an accurate time history of the flow is needed
d) only less memory is available
Explanation: Explicit methods are used to solve the Navier-Stokes equations when accurate time history of the flow variables is needed. The explicit time advancement method is more accurate than the first-order Euler method.
10. Which of these is correct for the implicit method of solving pressure in the compressible flows?
a) The Poisson equation alone is solved
b) The Poisson equation and the momentum equation are solved simultaneously
c) The momentum equation is solved first
d) The Poisson equation is solved first
Explanation: In the implicit method, the values in the previous time steps are altered after moving to the next step. The Poisson equation and the momentum equation are solved simultaneously here. No time-advancement is done here.
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