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Correct choice is (b) False

The best explanation: The coefficient of drag for a sphere that is kept at hypersonic FLOW is GIVEN by:

cd = \(\frac {D}{q_∞ S}\)

Where, S = πR^2 (R being the radius of the sphere)

This results in the value of cd being 1. CLEARLY, this RESULT is independent of the Mach number of the flow. The only CONDITION is that the Mach number should be in the range of hypersonic regime for this result to be valid.

The correct answer is (d) OBLIQUE shock METHOD

To elaborate: There are three other local surface inclination inclinations, in addition to Newtonian theory. Methods that are widely used to estimate distributions of pressure over HYPERSONIC BODIES are the tangent WEDGE method, tangent cone method and shock – expansion method.

Correct answer is (b) Increase monotonically

To elaborate: The lift/drag ratio for inviscid hypersonic flow over a flat plate is given by:

\(\FRAC {L}{D}\) = cotα

On plotting the curve, as the angle of attack decreases, L/D ratio monotonically INCREASES. Obviously this is a HYPOTHETICAL condition as SKIN friction drag is not incorporated in this.

Right CHOICE is (a) cd = \(\frac {D}{q_∞ S}\)

To elaborate: At HYPERSONIC speed, COEFFICIENT of DRAG over circular cylinder can be predicted using the Newton’s THEORY. It is given by:

cd = \(\frac {D}{q_∞ S}\)

Where, S = 2R is the cross – sectional area and R is the radius of the cylinder

cd = \(\frac {4}{3}\) which is obtained using Newton’s theory.

The CORRECT choice is (b) Zero

To explain: The Newtonian MODEL for fluid flow is only able to predict the coefficient of pressure in the FRONTAL region of the surface where the free stream IMPACTS the body. The portion which does not experience any IMPACT from the incoming flow is known to be in the shadow which has zero coefficient of pressure.

The correct CHOICE is (b) TANGENTIAL momentum

Easy explanation: When there is an incoming stream of particles on a flat plate with a FREE stream VELOCITY, the normal momentum is transferred to the surface after the impact. On the other hand, the tangential momentum is preserved. This result was obtained by Newton with an ASSUMPTION that the particles do not interact with each other and hence are linear.

The correct choice is (b) False

The BEST I can EXPLAIN: For three – dimensional bodies such as a cone, Newtonian theory is generally more accurate in contrast with two – dimensional bodies like wedge. One more important property to note is that Newton’s theory gets MUCH more accurate with increasing MACH number.

Right choice is (b) Finding pressure COEFFICIENT over BLUNT BODY

Easiest explanation: NEWTONIAN theory was developed in ORDER to predict the coefficient of pressure over the bluff body when there is incoming flow. It is given by the following relation:

Cp = 2sin^2θ

Where, the coefficient of pressure is given by:

Cp = \(\frac {1}{2} \frac {(p – p_∞)}{ρV^{2}}\)

Correct choice is (a) Pitching moment coefficient

The explanation: CHEMICALLY reactive flow in hypersonic flow determines the pitching moment over the space shuttle. The pressure on the FORWARD part of the shuttle BODY is usually higher for a chemically reactive gas, and it is lower in the rearward part. This LEADS to a positive pitching moment of the shuttle.

Correct option is (a) \(\frac {F}{A}\) = ρV\(_∞^2\)sin^2θ

The explanation is: For an incoming stream of particles over the inclined surface, the particles move ALONG the surface after the collision and hence the normal velocity is V∞sinθ. Where, θ is the angle formed between the incoming free stream velocity and the flat plate.

The RATE of mass flow of the particles over the flat inclined plate with an area A is given by ρAV∞sinθ.

Thus the force is given by product of mass flux and velocity change.

(ρAV∞sinθ)(V∞sinθ) = ρAV\(_∞^2\)sin^2θ = F

And since pressure is equal to force UPON area, therefore it is \(\frac {F}{A}\) = ρV\(_∞^2\)sin^2θ