A spacecraft is fueled using hydrazine (N2H4; molecular weight of 32 grams per mole [g/mol]) and carries 1 comma 630 kilogram
s [kg] of fuel. On a mission to orbit a planet, the fuel will first be warmed from negative 199 degrees Fahrenheit [°F] to 100 degrees Fahrenheit [°F] before being used after the long space flight to reach the planet. The specific heat capacity of hydrazine is 0.099 kilojoules per mole kelvin [kJ/(mol K)]. If there is 250 watts [W] of power available to heat the fuel, how long will the heating process take in units of hours [h]?
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Answer:
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Explanation:
Let suppose that fluid is incompressible and diffuser works at steady state. A diffuser reduces velocity at the expense of pressure, which can be modelled by using the Principle of Mass Conservation:
The following relation are found:
The new relationship is determined by means of linear interpolation:
After some algebraic manipulation, the following for the velocity as a function of position is obtained hereafter:
The acceleration can be calculated by using the following derivative:
The derivative of the velocity in terms of position is:
The expression for acceleration is derived by replacing each variable and simplifying the resultant formula.