A siphon(Fig. P12.88)is a convenient device for removing liquids from containers. To establish the flow, the tube must be initially filled with fluid. Letthe fluid has density r, and let the atmospheric pressure be patm . Assume that the cross-sectionalarea of the tube is the same at all points along it. (a) If the lower end of the siphon is at a distance hbelow the surface of the liquid in the container, what is the speed of the fluid as it flows out the lower end of the siphon? (Assume that the container has a very large diameter, and ignore any effects of viscosity.) (b) A curious feature of a siphon is thatthe fluid initially flows “uphill.” What is the greatest height Hthat the high point of the tube can have if flow is still to occur?

his height from small hole diameter.

$\sqrt{2gh}$is efflux speed from small hole.

Bernoulli's principle states that as the velocity of a liquid rises, the pressure falls, and when the speed lowers, the pressure increases.

We have to apply Bernoulli’s equation to fluid in the siphon.

As long as the water is still moving upward before exiting the syphon, it makes no difference to how fast it leaves.

The efflux speed is given as,

If the absolute (not gauge) pressure is negative, water will not flow. Even if the gauge pressure is negative, water will not flow. The bottom of the hose is exposed to the environment.

Pressure at the top of siphon is given as,

$p=p_a-\rho g\left(H+h\right)$

Here, cross-sectional is constant and is constant.

Putting, p = 0 in equation,

$H=\left(\frac{p_a}{\rho g}\right)-h$

But theresult shows $\left(H+h<\frac{p_a}{\rho g}\right)$. For water and normal atmospheric pressure, the value of $\frac{p_a}{\rho g}$ is 10.3 m .