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(D) Given: Diameter of orifice $D = 2 \,mm = 2 	imes 10^{-3} \,m$, Viscosity $\eta = 1 \,cP = 10^{-3} \,Pa \cdot s$, Density $ho = 10^3 \,kg/m^3$,

Vedclass · Accepted Answer

$11$

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(D) Given: Diameter of orifice $D = 2 \,mm = 2 	imes 10^{-3} \,m$, Viscosity $\eta = 1 \,cP = 10^{-3} \,Pa \cdot s$, Density $ho = 10^3 \,kg/m^3$, $g = 10 \,m/s^2$. For the flow to be turbulent, the Reynolds number $R_e$ should be greater than or equal to the critical value, typically taken as $R_e = 3000$. The Reynolds number is given by $R_e = \frac{ho v D}{\eta}$. Rearranging for velocity $v$: $v = \frac{R_e \eta}{ho D} = \frac{3000 	imes 10^{-3}}{10^3 	imes 2 	imes 10^{-3}} = 1.5 \,m/s$. Using Torricelli's Law, the velocity of efflux is $v = \sqrt{2gh}$. Squaring both sides: $v^2 = 2gh \Rightarrow h = \frac{v^2}{2g}$. Substituting the values: $h = \frac{(1.5)^2}{2 	imes 10} = \frac{2.25}{20} = 0.1125 \,m = 11.25 \,cm$. Rounding to the nearest integer, we get $11 \,cm$.

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