Problem $1(15$ p $)$: A fan is to accelerate quiescent air to a velocity of $18\frac{m}{s}$ at a rate of $4\frac{m^3}{m}in.$ If

the density of air is $1\mathrm{.}18k\frac{g}{m^3},$ determine the minimum power required to supply to the fan.

Problem $2(15p)$ : The engine of a truck develops $95$ kW of power. Determine the acceleration time of

this truck from rest to $70$mile$\frac{s}{h}$ on a level road. $($The mass of the truck is $1500$ kg $)$

Problem $3(30p)$ : Determine the power required for a $1500$ kg truck to climb a $250$ m long uphill road

with a slope of $30$ from the horizontal in $20$ s $($a$)$ at constant velocity $($b$)$ from rest to a final velocity of

$25\frac{m}{s}($c$)$ from $35\frac{m}{s}$ to a final velocity of $20\frac{m}{s}.$ Disregard friction, air drag, and rolling resistance.

Problem $4(40p)$ : A fluid at a pressure of $6$ atm with a specific volume of $0\mathrm{.}12m^{3}kg$ is constrained

in a cylinder behind a piston. It is allowed to expand reversibly to a pressure of $0\mathrm{.}9$ atm according to the

law $P=\frac{c}{V^{1\mathrm{.}75}},$ where c is a constant and V is the specific volume. Calculate the work done by the

fluid on the piston.