8. Three children, each weighing 500 N, decide to make a raft by lashing together logs of diameter 0.50 m and length 1.50 m. How many logs will they need to keep them afloat in fresh water? Take the density of each log to be 800 kg/m3.
9. A garden hose with an internal diameter of 2 cm is connected to a nozzle that has an exit hole with a diameter 0.1 cm in diameter. If the water enters the hose at 1 m/s, at what speed does it exit the nozzle?
Assuming the children and the logs are just afloat in water, then the logs will be fully submerged by the weight of the children.
Archimedes principle states that the upward buoyant force on a floating object is equal to the weight of the displaced water by the object.In this case, the force balance equations will be:
where n is the number of logs
The children need minimum 3 logs to stay afloat.
For a laminar flow of an incompressible fluid through a system, the Conservation of mass or Continuity equation gives:
As the inlet to the nozzle is a stream of water with circular cross-section and uniform velocity of 1 m/s, and outlet is also a uniform stream of water, assuming laminar flow throughout and thus applying continuity equation gives:
The water exits the nozzle with a speed of 400 m/s.
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