You need to siphon water from a clogged sink with 2.0cm wide hose. The 50 cm dee

Question

You need to siphon water from a clogged sink with 2.0cm wide hose. The 50 cm deep sink has an area of 0.50m2 and is filled to nearly overflowing. The siphon is broken when there is only 4.0 cm of water in the tank. a) Assuming that the water enters the siphon tube with almost zero velocity, calculate the velocity when it enters the pail. Do an example for both the full sink and nearly empty sink. b) Estimate how long it will take to empty the sink using the average of the 2 velocities calculated in part a.

Explanation / Answer

According to the problem,

Volume of water in sink = (0.50)(0.02) = 10^-3 m³

Water velocity entering pail = V = 2gh = (2)(9.8)(0.5) = 9.8 = 3.13 m/s [Full sink]

water velocity entering pail = U = 2gh = (2)(9.8)(0.04)) = 0.784

= 0.88m/s [nearly empty]

Average of speeds =((3.13+0.88)/2)

Area of siphon = (0.01)²/4 = 0.78 *10^-4 m²

volume rate of flow = (0.78 *10^-4 )* ((3.13+0.88)/2) = 1.56 * 10^-4 m³/s

Est. time to empty sink = 10^-3 /1.56 * 10^-4 = 6.41 s (b)

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