Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.60 m/s through a pipe 5.0 cm in diameter. Tire pipe tapers down to 2.6 cm in diameter by the top floor, 18 m above (Fig. 10–53), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in such a pipe on the top floor. Assume no branch pipes and ignore viscosity.
ANSWER:A)Mass of the car is 710 kg.Speed of the car is 23 m/s.Drag force is, F drag= 500 N .As there are various types of drag forces, the way of finding the power is same. So,the power required in the presence of drag force is, P = F × velocity ---------------------(1) d P = 500 × 23 = 11500 watts.This is the power required to move on the horizontal surface of ground.B) 0While riding the inclined hill which make s an angle of 3 with the horizontal, the things willbe changed a little.Here it has to overcome the frictional force with the drag force as well.As the normal reaction will cancel the vertical component of the force, only the mg Sin term will contribute for the frictional force.So the force the car has to overcome is, 0 F = mg sin + F D = (710 × 9.8 × sin 2 ) + 500 = 242.83 + 500 = 742.83N.\nAs we know the power is, P = F × velocity = 742.83 × 23 = 17085watts.So, the required power is 17085 watts.