Caveat: calculate the answers for BOTH part (a) and part (b) using the moment wh

Question

Caveat: calculate the answers for BOTH part (a) and part (b) using the moment when the sink has only 2cm of water in it

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 = 70 cm to a pail as shown in the figure. The siphon tube has a diameter of 2.6 cm.

Questions and diagram are supplied in the following diagram


http://imageshack.us/f/21/quest2u.png/

Explanation / Answer

Area of sink A = 0.48 m2
Height of water in sink h = 0.04 m
Diameter of siphon tube ( d ) = 0.026 m
Let us choose the reference level at the bottom of the sink.
According to the Bernoulli's equation
P1 + 1/2v12 + gh1 = P2 + 1/2v22 + gh2
Since at both ends pressure is same then
1/2v12 + gh1 = 1/2v22 + gh2
0 + gh1 = 1/2v22 + gh2
(0.5)v22 = gh
Therefore the velocity of water
v2 = gh
= 2(9.8 m/s2)(0.4 m)
= 2.8 m/s
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(b) Radius of the siphon tube is r = 1.3 cm
From equation of continuity
R = Av
V/dt = Av
(0.48 m2)(0.04 m)/t = (1.3 cm) 2 (1.98 m/s)
t = (0.48 m2)(0.04 m / (1.3 cm) 2 (2.8 m/s)
t = 12.92 s

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