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# MCQs on Hypersonic Similarity

Which of these does not result in two or more flows being dynamically similar?

a) Streamlines are geometrically similar

b) The shape of the blunt body is same

c) Length of the body is same

d) Non dimensional parameters remain same

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c

Explanation: Two or more flows are considered to be geometrically similar when the flow over the bodies remains identical. This happens when the shape of the bodies is identical and the variation in non – dimensional parameters remain same for the flows.

Why is hypersonic similarity parameter essential?

a) Supersonic flow over wedges

b) Hypersonic flow over slender bodies

c) Hypersonic flow over cone

d) Hypersonic flow over flat plate

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b

Explanation: Hypersonic similarity parameter K is an important governing parameter in order to study the hypersonic flow i.e. flow with Mach number greater than 5 over slender bodies. It is given by the product of free stream Mach number and flow deflection angle.

For two bodies with same shape but different scales, which of these parameters must be equal for the flow to be same in hypersonic regime?

a) Mach number

b) Product of Mach number and slenderness ratio

c) Tangential flow velocity

d) Normal flow velocity

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b

Explanation: The product of Mach number and slenderness ratio along with gamma are the two parameters which appear in the non – dimensional equations. For a body that has same shape but have different scale ratio, if these parameters are same, the flow over them at hypersonic regime remain same. This is the physical meaning of the hypersonic similarity parameter.

Two bodies holding hypersonic similarity at small angle of attack need the values of γ and M∞τ to be same.

a) True

b) False

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b

Explanation: For two bodies at hypersonic regime at very small angle of attack, apart from product of Mach number and slenderness ratio M∞τ and the value of gamma γ, there is one more condition to be met to have similar dynamic flow. That condition is that the ratio of angle of attack to slenderness ratio (α/τ) should be same.

The ratio Cpτ2 behind a shock wave is a function of which of these parameters?

a) Hypersonic similarity parameter K and γ

b) Angle of attack and wedge angle

c) Coefficient of lift and wedge angle

d) Hypersonic similarity parameter and angle of attack

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a

Explanation: For the flow over a wedge having slenderness ratio τ has formation of oblique shock waves. The relation is given by:

Cpτ2 = f(K,γ)

According to this, Cpτ2 is a function of only gamma and the hypersonic similarity parameter.

On which of this parameter is the coefficient of lift over a two – dimensional body at hypersonic flow dependent?

a) γ.ατ

b) γ, K, M∞

c) M∞T, ατ, γ

d) M∞T, K, γ

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c

Explanation: The lift coefficient over the body at hypersonic flow is obtained by integrating the pressure coefficient over the surface.

cl = 1l∫l0(Cpl – Cpu)dx

Where, Cpl – Cpu are coefficient of pressure over the upper and lower surface

l is the length of body

The above equation in terms of x is

cl = ∫10(Cpl – Cpu)dx

Diving this equation with the square of slenderness ratio, we get

clτ2=∫10(Cpl – Cpu)dx = f(M∞T, ατ, γ)

Thus, coefficient of lift is a function of M∞T, ατ and γ.

Hypersonic similarity is applicable for only irrotational flow.

a) True

b) False

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b

Explanation: While deriving for hypersonic similarity using the governing equations for hypersonic flow, there is no assumption made for rotational or irrotational flow. Thus, when the graph is plotted for both rotational and irrotational flow for different values of freestream velocity and slenderness ratio, both the graphs are same.

For which range of values is the hypersonic similarity rule valid for very slender bodies?

a) K = 0.5 to infinity

b) K > 1.5

c) 0.5 < K < 1.5

d) 2 < K < 1000

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a

Explanation: Hypersonic similarity condition does not hold true for all values of K. For bodies which are very slender such as the cone having half angle of 3 degrees, the similarity stays valid only when the value of K ranges from 0.5 to infinity.