Question

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?

Answer 1

Answer:

0.02 m/s

Explanation:

using the formula for flow rate

Q = V / t = Av

v ( speed) = V/ ( TA) where V is volume in m³, t is in seconds, and A is area of the 3.0 cm diameter

V = length × breath × height = 0.36 m × 1.0 m × 0.60 m = 0.216 m³

Area = πr² = π ( 0.03 / 2)² = 0.00071 m²

t = 4 × 60 × 60 = 14400 s

substitute the values into the equation

v =   0.216 m³ / ( 14400 s × 0.00071 m² ) = 0.02 m/s

Answer 2

The flow speed in the 3.0-cm-diameter input tube for the filter is 0.021 m/s

Width of tank = 36 cm = 0.36 m

Volume of tank (V) = length * width * height = 1 * 0.36 * 0.6 = 0.216 m³

Diameter = 3 cm = 0.03 m; radius = diameter / 2 = 0.015 m

Area (A) = πr² = π(0.015)² = 7.07 * 10⁻⁴ m²

Time (t)  = 4 hour = 4 * 3600 s = 14400 seconds

The flow speed (v) is:

$v=\frac{V}{At}=\frac{0.216}{7.07*10^{-4}*14400}=0.021$

Therefore the flow speed in the 3.0-cm-diameter input tube for the filter is 0.021 m/s

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