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 4.0 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?

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5. 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

To find the flow speed in the input tube for the filter, we need to determine the volume of water in the tank and divide it by the time it takes for the filter to process that volume.

First, let's calculate the volume of water in the fish tank:
Volume = length × width × height
Volume = 1.0 m × 0.36 m × 0.60 m
Volume = 0.216 cubic meters

Next, we need to convert the volume from cubic meters to liters since the flow rate is usually measured in liters per hour:
1 cubic meter = 1000 liters
Volume = 0.216 cubic meters × 1000 liters/cubic meter
Volume = 216 liters

Now, divide the volume by the time it takes for the filter to process that volume:
Flow rate = Volume / Time
Flow rate = 216 liters / 4.0 h
Flow rate = 54 liters/hour

Finally, we need to convert the flow rate from liters/hour to centimeters/second. Since we have the diameter of the input tube, we can use the formula to calculate the flow speed of a liquid through a pipe:
Flow speed = Flow rate / (π × (input tube diameter/2)^2)
Flow speed = 54 liters/hour / (π × (3.0 cm / 2)^2)

Now, let's calculate the flow speed:
Flow speed = 54 liters/hour / (π × (1.5 cm)^2)
Flow speed ≈ 54 liters/hour / (3.14 × 2.25 cm^2)
Flow speed ≈ 54 liters/hour / 7.065 cm^2
Flow speed ≈ 7.64 cm/hour

Therefore, the flow speed should be approximately 7.64 cm/hour in the 3.0-cm-diameter input tube for the filter.

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