When you vomit your stomach forces a fluid flow from your mouth. 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

The gauge pressure as calculated is 5862.36 Pa

Solution:

As per the question:

Radius, r = 1 cm = 0.01 m

Length, l = 60 cm = 0.6 m

Velocity of discharge of fluid from the mouth, v = 1.5 m/s

Now,

By using the continuity equation:

Av = A'v'                       (1)

where

A = Area of the mouth

A' = Area of the tube

v' = Velocity of the fluid inside the stomach

Since, the question assumes the stomach, mouth and esophagus as continuous vertical tube, then:

A = A'

Thus

From eqn (1):

v = v' = 1.5 m/s

Now,

With the help of Bernoulli's equation:

where

h - h' = l = 60 am = 0.6 m

P = Pressure at mouth = 1 atm =

g = acceleration due to gravity

Density of water,

P' = Pressure inside the stomach

P' - P = Gauge Pressure

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