Question

Treating your stomach, esophagus, and mouth as a continuous vertical tube of radius 1 cm and length 60 cm, what gauge pressure must your stomach generate to cause vomit to move at 1.5 m/s out of your mouth, in Pa?  Assume the vomit has the density of water.

Answer 1

By continuity equation,

A1*V1 = A2*V2

here, A1 = area of mouth

A2 = area of tube in stomach

V1 = velocity at mouth

V2 = velocity in stomach

given, A1 = A2

So, V1 = V2 = 1.5 m/s

By Bernoulli's equation,

P1 + 0.5*rho*V1^2 + rho*g*h1 = P2 + 0.5*rho*V2^2 + rho*g*h2

P1 = pressure at mouth = 1atm = 1.01325*10^5 Pa

rho = density of water = 997 kg/m^3

g = 9.81 m/s^2

P2 = pressure in stomach

h1 - h2 = length of tube = 60 cm = 0.6 m

So, Gauge pressure = P2 - P1 = 0.5*rho*V1^2 - 0.5*rho*V2^2 + rho*g*(h1-h2)

P2 - P1 = rho*g*(h1-h2) = 997*9.81*0.60

P2 - P1 = 5868.342 Pa

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