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# MCQs on Time-Marching Technique – Newtonian Theory

What is a Newtonian theory used for?

a) Finding lift coefficient over blunt body

b) Finding pressure coefficient over blunt body

c) Finding drag coefficient over sharp wedge

d) Finding pressure coefficient over cone

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b

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 = 2sin2θ

Where, the coefficient of pressure is given by:

Cp = 12(p–p∞)ρV2

Newton theory is applicable for which of these flows?

a) Subsonic flow

b) Supersonic flow

c) Transonic flow

d) Hypersonic flow

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d

Explanation: Newton’s theory is more accurate for hypersonic flows with Mach numbers greater than 5. This is because as the free stream Mach number increases and the angle between free stream and inclined flat plate increases, the accuracy of Newtonian theory also increases.

What is the relation according to the Newton’s theory for hypersonic problems?

a) Cp = 2sinθ

b) Cp = 2sin2θ

c) Cp = cosθ

d) Cp = 2sinθcosθ

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b

Explanation: By using the relation of oblique shock theory and applying the limits M∞ → ∞ because hypersonic flows theoretically range from Mach number = 5 to infinity and γ → 1, we get the result for Newtonian theory. It is given by:

Cp = 2sin2θ

Where, θ is the local inclination angle of the surface with respect to the free stream velocity.

According to the Newtonian theory, which of these is preserved after the impact of the incident particles?

a) Normal momentum

b) Tangential momentum

c) Normal velocity

d) Tangential velocity

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b

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.

According to the Newtonian model for fluid flow, what is the coefficient of pressure at the rear of the surface while free stream flows horizontally towards it?

a) One

b) Zero

c) Infinity

d) 0.5

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b

Explanation: 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.

According to Newton’s theory, what happens to the lift to drag value with decreasing angle of attack of a flat plate?

a) Remains same

b) Increase monotonically

c) Decreases parabolically

d) Becomes zero with maximum angle of attack

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b

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

LD = 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.

At what angle does the coefficient of lift over a flat plate become maximum?

a) 66.6 deg

b) 54.7 deg

c) 33.3 deg

d) 90 deg

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b

Explanation: According to the Newton’s theory, the coefficient of lift is given by:

cl = 2sin3α

This value is maximum for α = 54.7 degrees.

What is the formula for coefficient of drag over a circular cylinder at hypersonic speed?

a) cd = Dq∞S

b) cd = D2q∞S

c) cd = 2Dq∞S

d) cd = Dq∞S

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a

Explanation: At hypersonic speed, coefficient of drag over circular cylinder can be predicted using the Newton’s theory. It is given by:

cd = Dq∞S

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

cd = 43 which is obtained using Newton’s theory.

Coefficient of drag over a sphere at hypersonic speed is dependent on the Mach number.

a) True

b) False

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b

Explanation: The coefficient of drag for a sphere that is kept at hypersonic flow is given by:

cd = Dq∞S

Where, S = πR2 (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.

What is the pressure exerted by the incoming stream of particles on an inclined flat plate based on Newton’s theory?

a) FA = ρV2∞sin2θ

b) FA = ρV∞sin2θ

c) FA = ρV2∞cos2θ

d) FA = ρV2∞sinθ

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a

Explanation: 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) = ρAV2∞sin2θ = F

And since pressure is equal to force upon area, therefore it is FA = ρV2∞sin2θ

Newton’s theory gives much more accurate results for 2 – dimensional shapes.

a) True

b) False

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b

Explanation: 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.

Which of these methods is not a local inclination method for computing pressure distribution?

a) Newtonian theory

b) Tangent wedge theory

c) Tangent cone theory

d) Oblique shock method

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d

Explanation: 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.

As a result of chemically reacting gas, which of these features differ compared to the ideal gas??

a) Pitching moment coefficient

b) Temperature

c) Drag

d) Lift

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a

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.