Engineering Questions with Answers - Multiple Choice Questions

# Aerodynamics – Two Dimensional Irrotational Flow

1 - Question

What is the value of derivative of flow field along characteristic line?
a) Zero
b) Indeterminate
c) One
d) 0.5
Explanation: If we consider the direction along the flow field and take the derivatives of these flow properties, the value takes the form of numeratordenominator=00 or indeterminate form along the characteristic lines.

2 - Question

Which of these equations defines the characteristic curve in an x – y plane?
a) dydxchar=−uva2±(u2+v2a2)–11–u2a2
b) dydxchar=−uva2±(u2+v2a2)√u2a2
c) dydxchar=–uva2±(u2+v2a2)−1−−−−−−−−−√
d) dydxchar=−uva2±(u2+v2a2)−1√1–u2a2
Explanation: The approach of method of characteristics entails determining special curves, referred to as characteristics curves, along which the PDE transforms into a family of ordinary differential equations (ODE). If the ODEs have been identified, they can be solved along the characteristic curves to obtain ODE solutions, which can then be compared to the original PDE solution. The characteristic curve is given by: dydxchar=−uva2±(u2+v2a2)−1√1–u2a2

3 - Question

How many characteristics pass through a point in the flow field if the Mach number is greater than 1?
a) 1
b) 2
c) 4
d) 0
Explanation: The characteristic curve is given by the relation dydxchar=−uva2±(u2+v2a2)−1√1–u2a2 The term inside the square root u2+v2a2 – 1 can be written in the form of Mach number as follows: u2+v2a2 – 1 = V2a2 – 1 = M2 – 1 When the flow is supersonic i.e. Mach number is greater than 1, two characteristics pass through a point in a flow field. Hyperbolic partial differential equation is used to define it.

4 - Question

Which partial differential equation is used to define the characteristic at sonic condition?
a) Hyperbolic partial differential equation
b) Parabolic partial differential equation
c) Elliptic partial differential equation
d) Circular partial differential equation
Explanation: At sonic condition, when Mach number is equal to 1, there is only one characteristic that passes through the flow field point. This is defined by the parabolic partial differential equation. dydxchar=−uva2±M2–1√1–u2a2

5 - Question

For subsonic flows, the characteristics through a flow field point are imaginary.
a) True
b) False
Explanation: When the Mach number is less than 1 i.e. the flow is subsonic, the numerator in the characteristic curve is imaginary as the terms inside the square root sign is negative. Thus, methods of characteristics is not used for subsonic flows. dydxchar=−uva2±(−veterm)√1–u2a2

6 - Question

How many characteristic lines pass through the flow field in supersonic flow?
a) 1
b) 2
c) 0
d) 4