First slide

Fluid dynamics

Question

A siphon has a uniform circular base of diameter $\frac{8}{\sqrt{π}} cm$ with its crests 1.8 m above water level as in figure. The absolute pressure at the crest level A(in kPa) is__________. $[U s e P_{0} = 10^{5} N / m^{2} and g = 10 m / s^{2}]$

Moderate

Solution

$Velocity of flow = \sqrt{2 g h} = \sqrt{2 \times 10 \times 3.6} = 6 \sqrt{2} m / s$
Bernoulli's theorem between surface and A
$\begin{array}{l} P_{atm} = P + \frac{1}{2} ρ v^{2} + ρ g h \\ P = P_{atm} - \frac{1}{2} ρ v^{2} - ρ g h \\ = 10^{5} - \frac{1}{2} \times 10^{3} (6 \sqrt{2})^{2} - 10^{3} \times 10 \times 1.8 \\ = 4.6 \times 10^{4} N / m^{2} = 46 kPa \end{array}$

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