You need to siphon water from a clogged sink. The sink has an area of 0.52 m 2 a

Question

You need to siphon water from a clogged sink. The sink has an area of 0.52m2 and is filled to a height of 4.0 cm. Your siphon tube rises 45 cm above the bottom of the sink and then descends 85 cm to a pail as shown in the figure (Figure 1) . The siphon tube has a diameter of 1.9cm . Ignore viscosity.

A. The tube in the pail is about 4.0 cm below the surface of the liquid in the pail. Assuming that the water level in the sink has almost zero velocity, use Bernoullis equation to estimate the water velocity when it enters the pail.

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

You need to siphon water from a clogged sink. The sink has an area of 0.52m2 and is filled to a height of 4.0 cm. Your siphon tube rises 45 cm above the bottom of the sink and then descends 85 cm to a pail as shown in the figure (Figure 1) . The siphon tube has a diameter of 1.9cm . Ignore viscosity. The tube in the pail is about 4.0 cm below the surface of the liquid in the pail. Assuming that the water level in the sink has almost zero velocity, use Bernoulli's equation to estimate the water velocity when it enters the pail. Estimate how long it will take to empty the sink.

Explanation / Answer

We can say, by Bernoulli's Principle, that...

pg(h2 - h1) = .5pv^2

v = sqrt (2gh)

v = sqrt [(2)(9.8)(.4)]

v = 2.8 m/s

The volume of water in the sink is (.52)(.04) = .0208

.0208

The volume flow rate = Av = (pi)(9.5 X 10^-3)^2(2.8) = 7.94 X 10^-4 m^3/s

.0208/7.94 X 10^-3 = 26.2 sec

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