A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height (in cm) of the water above the orifice for which the output flow of water is found on be turbulent ?________________
(Assume g= 10 m/s², $ρ_{water}$ =10³ kg/m³, viscosity = 1 centi-poise)

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answer is 20.

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Detailed Solution

Given,

The diameter,

$D = 2 mm,$

$η = 1 centi - poise = 10^{- 3} Pa - s$

$density of the water, ρ = 10^{3} kg / m^{3}$

$For flow to be just turbulent R_{e} = 2000$

Critical velocity (beyond which the flow turns turbulent) is

$v_{c} = \frac{R_{e} η}{ρd} \Rightarrow v_{c} = \frac{2000 \times 10^{- 3}}{10^{3} \times 2 \times 10^{- 3}} \Rightarrow v_{c} = 1 {ms}^{- 1}$

The velocity,

$h = \frac{v^{2}}{2 g} = \frac{1^{2}}{2 \times 10} = 0.05 = 5 cm$

Hence the correct answer is 5.

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