You need to siphon water from a clogged sink. The sink has an area of 0.485 m 2

Question

You need to siphon water from a clogged sink. The sink has an area of 0.485 m2 and is filled to a height of 4.0 cm. Your siphon tube rises 50 cm from the bottom of the sink and then descends h = 101 cm to a pail as shown above. The siphon tube has a diameter of 1.58 cm.
a. Assuming that the water enters the siphon with almost zero velocity, calculate its velocity when it enters the pail. (You may assume the tube is maintained above the water surface in the pail, not exactly as shown in the picture.)
v =

b. Estimate how long it will take to empty the sink.

T =

Please give solution as well as answer for full points.

Explanation / Answer

Part A)

The pressure is essentially the same in both cases, so we can set up Bernoulli's Equation as

pgh + .5pv^2 = pgh + .5pv^2

We are told that the velocity at the inlet can be considered zero. We can also consider the heigt of the end of the tube going into the bucket as zero, so

(1000)(9.8)(.51) = (.5)(1000)(v^2)

v = 3.16 m/s

Part B)

The total volume of the water is (.485)(.04) = .0194 m^3

The area of the the syphon is pi(r^2) = pi(7.9 X 10^-3)^2 = 1.96 X 10^-4 m^2

The time is found using V/Av

.0194/(1.96 X 10^-4)(3.16) = 31.3 sec

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