Problem 3: A fish tank has a diameter of 0.30 m 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 hours, what should the flow speed be in the 3.0 cm diameter input tube for the filter<

Solution

A tank-full volume of water flows in 3 h. So, we should find the volume of water = volume of the tank, and then find the flow speed of the volume of water using formula, Av = ΔV/Δt. Here v is the speed of water and V is the volume of water.
Now volume of the tank = ℓ × h × w = 1 × 0.6 × 0.30 = 0.18 m^{3} = ΔV. Time, Δt = 3 h = 3 × 60 × 60 = 10800 s. Diameter of the pipe = 3.0 cm = 0.03 m ⇒ radius of the pipe = (0.03/2) = 0.015 m. Apply formula, A = πr^{2} to find the cross-sectional area of the pipe.

Now apply formula Av = ΔV/Δt to find the flow rate.

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