Question

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? assume the vomit has the density of water.

Answer 1

The stomach must generate a gauge pressure of 1125 Pa to cause vomit to move at a speed of 1.5 m/s out of the mouth, assuming the density of vomit is the same as water.

Step-by-step explanation:

To determine the gauge pressure that the stomach must generate to cause vomit to move at a speed of 1.5 m/s out of the mouth, we can apply Bernoulli's equation.

The equation for fluid flow due to a pressure difference in a tube is given by

∆P = ½ρv2,

where ∆P is the gauge pressure, ρ is the density of the fluid, and v is the speed of the fluid flow. Since the density of water (and similarly the vomit, as given in the problem) is 1000 kg/m3, we can calculate the required gauge pressure.

∆P = ½(1000 kg/m3)(1.5 m/s)2 = ½(1000)(2.25) = 1125 Pa

Thus, the stomach must generate a gauge pressure of 1125 Pa to allow for the vomit to exit the mouth at the given speed.