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Mohamed S.

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Mechanical Engineering

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Question:

What is the definition of the Compression Ratio in internal combustion engines?

Mohamed S.

Answer:

The Compression ratio is the ratio between the cylinder volumes at the Bottom Dead Center to that at the Top Dead Center. And is equal to the ratio between the summation of the clearance volume plus swept volume over the clearance volume. Also equal to 1 + (swept volume / clearance volume).

Calculus

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Question:

Solve the following differential equation and state its type: dY / dX = Y+1 / X+3

Mohamed S.

Answer:

This is an Ordinary, First Order, Separable Differential Equation and its solution will be as follows: * By Separating the variables, gives: dY / Y+1 = dX /X+3 * Then, by integration for both sides, gives : ln ( Y + 1 ) = ln ( X + 3 ) + C (where C is an arbitrary constant) *Finally, by further simplification, gives: ln [( Y+ 1 ) / ( X + 3 )] = C [( Y + 1 ) / ( X + 3 )] = exp(C) Y = [X*exp(C)] + [3*exp(C)] - 1

Algebra

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Question:

Solve the following system of equations: x + 2y +4z = 10 2x +5y +10z = 51 5x +2y + z = 12

Mohamed S.

Answer:

X = -52 Y = 171 Z = -70

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