A siphon, as shown in the figure (Figure 1) , is a convenient device for removin
ID: 1587122 • Letter: A
Question
A siphon, as shown in the figure (Figure 1) , is a convenient device for removing liquids from containers. To establish the flow, the tube must be initially filled with fluid. Let the fluid have density , and let the atmospheric pressure be pa. Assume that the cross-sectional area of the tube is the same at all points along it.
Part A
If the lower end of the siphon is at a distance h below 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.)
Part B
A curious feature of a siphon is that the fluid initially flows "uphill." What is the greatest height H that the high point of the tube can have if flow is still to occur?
Express your answer in terms of the given quantities and appropriate constants.
Explanation / Answer
a) The pressure at the top of the liquid in the container is P0= Patm , the same as it is at the lower end of the tube. Applying Bernoulli’s equation with points “1” and “2” at the top of the liquid in the container and the lower end of the tube, respectively, we have
P0+ 1 /2 v12 + gh =P0+ 1 /2 v22,
v22 = v12 + 2gh.
But with a very large container we can assume that v1 0 and
v2 =(2gh)1/2
(b) The pressure at the high point of the tube can be related to that at its low end with
P = P0 g(H + h)
The liquid will not flow if the absolute pressure is negative anywhere in the tube, since a zero absolute pressure would imply that a perfect vacuum be present at that point. We then write
P0 g(H + h) > 0
or
H < (P0 / g) h. --------------(1)
We note that equation (1) also implies a limitation on H + h , which for water and normal atmospheric pressure yields
H + h < Patm /g
<10.3 m.