To ensure proper circulation of water in a swimming pool, water enters through submerged jets and spills into a trough around the sides of the pool. If one holds one's hand or a flat plate perpendicular to the jet and a short distance from the nozzle exit as in Figure A, the force of the jet can be felt. Similarly, by pushing one's hand or a flat plate against the end of the nozzle to stop the flow as in Figure B, the force due to the water pressure in the nozzle can be felt. Are these two forces the same? Consider nozzles 30 mm in diameter and a differential pressure head between the water in the supply pipe and the water in the pool of 2 m head.

Calculate the force due to the jet when the plate is a short distance away from the nozzle (approximately 50 mm).

Calculate the force due to the water pressure when the plate is against the nozzle and there is no flow from the nozzle.

Neglect friction effects and turbulence between the jet and the surrounding water.