You need to siphon water from a clogged sink. The sink has an area of 0.462 m2 a

Question

You need to siphon water from a clogged sink. The sink has an area of 0.462 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 = 96 cm to a pail as shown above. The siphon tube has a diameter of 2.1 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.)

HELP: Use Bernoulli's principle.
HELP: Do not neglect the pressure contribution from the depth (4.0 cm) of the water in the sink

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

HELP: For a quick estimate, assume the depth of water in the sink is an intermediate value, i.e. 2.0 cm.

Explanation / Answer

a.) p*g*y1 + 0.5*p*v1^2 = p*g*y2 = 0.5*p*v2^2

g*(0.96-0.5+0.04) + 0 = 0 + 0.5*v2^2

So v2^2 = 2*g*0.5

So v2 = 3.13 m/s

b.)Flowrate = v2*A2 = 3.13*pi*(0.0105)^2 = 1.084 x10^-3 m^3/s

Volume of water = 0.462*0.04 = 0.01848 m^3

So time = Volume/Flowrate = 17.05 seconds

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