You need to siphon water from a clogged sink. The sink has an area of 0.60 m2 an

Question

You need to siphon water from a clogged sink. The sink has an area of 0.60 m2 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 1.9 cm . Ignore viscosity.

1. 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.

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

Explanation / Answer

1) Volume of water in sink = (0.60)(0.04) = 0.024 m³ =240e-4 m³
Water velocity entering pail = V = 2gh = (2)(9.8)(0.85) = 16.66 = 4.08 m/s

2) Area of siphon = (0.019)²/4 = 2.84e-4 m²
volume rate of flow = (2.84e-4)(4.08) = 11.57e-4 m³/s
Est. time to empty sink = 240e-4/11.57e-4 = 20.74 s

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