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.

a) 29,400 Pa
b) 22,000 Pa
c) 14,700 Pa
d) 7,350 Pa

Answer 1

The gauge pressure that the stomach must generate to cause vomit to move at 1.5 m/s out of the mouth is 1120.24 Pa. Hence, none of the given options are correct.

Step-by-step explanation:

To determine the gauge pressure needed for vomit to move at a certain speed, we can use Bernoulli's equation for fluid flow. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume is constant along a streamline.

In this case, since the vomiting process involves the fluid moving through a vertical tube, we only need to consider the potential energy term.

The potential energy of the fluid is given by the formula P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height or distance the fluid moves against gravity.

Since the vomit is moving at a speed of 1.5 m/s, we can calculate the height using the formula h = v^2 / (2g), where v is the velocity and g is the acceleration due to gravity.

Substituting in the values, we get h = (1.5^2) / (2 * 9.8) = 0.1148 m.

To convert this height to pressure, we multiply by the density of water.

The density of water is 1000 kg/m^3, so the pressure is P = ρgh = (1000 * 0.1148 * 9.8) = 1120.24 Pa.

Therefore, the gauge pressure that the stomach must generate is 1120.24 Pa.