A fish tank has dimensions 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 h, what should the flow speed be in the 3.0 cm diameter input tube for the filter? (2.4 cm/s) 


Given:

Width of tank = w = 0.3 m
Length of tank = l = 1.0 m
Height of tank = h = 0.60 m so,
Time for processing all water = t = 3 h = 3 ｘ 3600 s = 10800 s
Diameter of input tube = d = 3.0 cm = 0.03 m

To Find:

Speed of water flow = v = ?

Solution:

From the equation of continuity, the rate of volume flow is given by the relation

`\frac {ΔV}{Δt}` = A v

or 

v =  `\frac {ΔV}{AΔt}` -----------(1)

Here we have to find the Area (A) and Volume (V) of the tank which are

 A = 𝜋 r² = = 𝜋 (d/2)² = 𝜋 (0.03 m / 2)² = 0.0007 m²

and 

V = w ｘ l ｘ h = 0.3 m ｘ 1.0 m ｘ 0.60 m = 0.18 m³

So putting values in equation (1) 

v =  `\frac {0.18 m³}{0.0007 m² ｘ 10800 s}`

v = 0.0238 m s⁻¹

or

v = 2.38 cm s⁻¹  --------------- Ans.


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