You need to siphon water from a clogged sink. The sink has an area of .48m^2 and

Question

You need to siphon water from a clogged sink. The sink has an area of .48m^2 and is filled to a height of 4.0cm. You siphon tube rises 50 cm above the bottom of the sink and then descends 100 cm to a pail. The siphon tube has a diameter of 2.0 cm. a) Assuming that the water enters the siphon tube with almost zero velocity, calculate its velocity when it enters the pail. b) Estimate how long it will take to empty the sink. c) Earth's atmospheric mass density decreases exponentially with altitude above sea level, at a rate of approximately 50% every 5.6 km (e.g.- approximately half of the atmospheric mass is below 5.6 km altitude). Determine the atmospheric pressure at 5.6 km altitude above sea level.

Explanation / Answer

Volume of water in sink = (0.48)(0.04) = 0.0192 m³ = 192e-4 m³ Water velocity entering pail = V = v2gh = v(2)(9.8)(0.7) = v13.72 = 3.7 m/s ANS A) Area of siphon = p(0.016)²/4 = 2.01e-4 m² volume rate of flow = (2.01e-4)(3.7) = 7.44e-4 m³/s Est. time to empty sink = 192e-4/7.44e-4 = 26 s ANS B)

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