Question

A water tank kept on the ground has an orifice of $2 \,mm$ diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent? (Assume, $g=10\, m / s ^{2}, \rho_{\text {water }}=10^{3} \,kg / m ^{3}$ viscosity = 1 centi-poise )

• A. 3 cm
• B. 4 cm
• C. 6 cm
• D. 2 cm

Answer 1

Answer: (A), (B), (C), (D)

Here, $D=2 \,mm , \,\eta=1$ centi-poise $=10^{-3} \,Pa - s$
and density of the water, $\rho=10^{3} \,kg / m ^{3}$
For flow to be just turbulent, $R_{e}=3000$
$\therefore \, v=\frac{R_{e} \eta}{\rho D}=\frac{3000 \times 10^{-3}}{10^{3} \times 2 \times 10^{-3}}=1.5$
We know that the velocity head, $h=\frac{v^{2}}{2 g}$
$\Rightarrow \, h=\frac{(1.5)^{2}}{2 \times 10}=0.1125 \simeq 11 \,cm$