You need to siphon water from a clogged sink. The sink has an area of 0.48 m 2 a

Question

You need to siphon water from a clogged sink. The sink has an area of 0.48 m2 and is filled to a height of 4.0 cm. Your siphon tube rises 50 cm above the bottom of the sink and then descends a distance h = 100 cm to a pail as shown in the figure. The siphon tube has a diameter of 2.4 cm.

(a) Assuming that the water level in the sink has almost zero velocity, estimate its velocity when it enters the pail.

_______________ m/s

(b) Estimate how long it will take to empty the sink.
_________________ s

You need to siphon water from a clogged sink. The sink has an area of 0.48 m2 and is filled to a height of 4.0 cm. Your siphon tube rises 50 cm above the bottom of the sink and then descends a distance h = 100 cm to a pail as shown in the figure. The siphon tube has a diameter of 2.4 cm. Assuming that the water level in the sink has almost zero velocity, estimate its velocity when it enters the pail. Estimate how long it will take to empty the sink.

Explanation / Answer

Given : Area of sink A = 0.48 m2 Height of water in sink h = 0.04 m
Diameter of siphon tube ( d ) = 0.024 m We choose the reference level at the bottom of the sink. (a) Applying the Bernoullis princeple, P1+ mgh1+ 1/2*rho*v1^2 = P2+ mgh2 + 1/2*rho*v2^2 P1=P2= atm P 1/2v2^2 = g (?h) 1/2v2^2 = g (?h) v2^2 = 2*9.8(0.5) v2 = 3.13 m/s (b)Using the equation of continuety, (A1V1) = A2V2 volume of the sink/t = A2V2 (0.48*0.04)/t =[pi* (0.02)^2 *3.13]/4 t = 19.53 s the time to empty sink is 19.53 s.

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