A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 3.0 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?
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This is Giancoli Answers with Mr. Dychko. The volume rate of flow is gonna be the volume of the fish tank divided by the time in which that whole volume has to be processed by this filter and volume rate of flow is also the area of the hose going into the end of the pump times the speed of water going through it. So we can solve for the speed by dividing both sides by the area and that will give the volume divided by area times time and so that's 0.36 meters by 1.0 meter by 0.60 meters—dimensions of the tank— divided by π times r squared and the radius is the diameter 3.0 times 10 to the minus 2 meters so expressing the diameter in meters instead of centimeters, dividing that by 2 and then squaring that then times by 3 hours times 3600 seconds per hour, hours cancel and we get seconds there and we have 0.028 meters per second or 2.8 centimeters per second.
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