A drinking straw 20 cm long and 3.0 mm in diameter stands vertically in a cup of

Question

A drinking straw 20 cm long and 3.0 mm in diameter stands vertically in a cup of juice 8.0 cm in diameter. A section of straw 6.4 cm long extends above the juice. A child sucks on the straw, and the level of juice in the glass begins dropping at 0.18 cm/s

A) By how much does the pressure in the child's mouth differ from atmospheric pressure? (ans = 1.43%)

B) What is the greatest height from which the child could drink, assuming this same mouth pressure? (ans = 14.8 cm)

How do you get to the answer? I'm trying to understand the concept(s) behind this problem.

Explanation / Answer

1. Let pressure inside the child's mouth be P
From bernoulli's theorem, P + 0.5*rho*v^2 + rho*g*h = Po + 0.5(rho)*(0.0018)^2 ( h = 0.064 m)
Now, from continuity equation, A1V1 = A2V2
pi*0.04^2*0.0018 = pi*(0.0015)^2*v
v = 1.28 m/s
so, P - Po = 0.5*rho*(-1.6383 - 1.2544)
Po - P = rho*1.44635 pa ( where rho is density of juice)
now if ans = 1.43 pc
(Po - P)/Po = 0.0143 = 1.46635*rho/1.1*10^5
rho = 1072.731 kg/m^3
Po - P = 151.5453 Pa
2. P + (rho)gh' = Po + 0.5(rho)*0.0018^2[ h' is max hieght, and we assumed v = 0]
151.5453 = 1072.731*9.8*h - 0.5(1072.731)(0.0018^2)
h' = 14.75 cm

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