Fluid dynamics question

Question

A siphon is being used to drain water from a clogged sink. The sink has an area of 0.48 m2 and is filled to a height of 4 cm. The siphon tube rises 50 cm above the bottom of the sink and then descends 100 cm to a pail as shown in the figure. The siphon tube has a diameter of 2.0 cm. (a) Assuming that water enters the siphon with almost zero velocity, calculate the velocity when it exits into the pail. Estimate how long it will take to empty the sink. BTW, the water in the pail is 100 cm below the top of the sink.

How do you solve? I understand that the bernoulli's equation is first applied to find the velocity. However, I do not understand how to solve the time. Time = velocity/distance right? Isn't velocity according to bernoulli's equation equal to the top and bottom? I am very confused.

Answer 1

bernoulli's principle does not require water to be the same velocity on both ends:

rho*g*h + .5*rho*v² initial = rho*g*h + .5*rho*v² final and initially velocity is zero so it cancels out on left side of equation.

For time use the formula that A1V1=A2V2 from cons. of mass. Note that A1V1 is Area*distance/time and the distance its moving is downward so the base area times the height it moves through over time so it's really volume/time so volume flow rate so set the volume/time = A2V2