A fire truck connects a large-diameter hose to a fire hydrant, and then shoots water out of a nozzle connected to a smaller-diameter hose. Point 1 is in the large-diameter hose right before it enters the fire truck. Point 2 is in the small-diameter hose right after it leaves the fire truck (at the same height as point 1). The gauge pressure at point 1 is 300 kPa, the diameter of the large-diameter hose is 14.6 cm, and the flow rate through it is 8.7 L/s. The diameter of the small-diameter hose is d. The hoses are both short enough, and wide enough, that we can neglect the pressure drops due to resistance.
What is the speed of the water at point 1 in the large-diameter hose? Enter your answer in m/s to 2 decimal places.
Water shoots out of the nozzle into the air, to land on the fire. If the nozzle is 23.6 m above the fire truck, what is the gauge pressure at point 2 in the small-diameter hose?
What is the speed of the water at point 2 in the small-diameter hose?
What is the diameter of the smaller hose, d?