Calculating Pressure Drop in a Bronchial Constriction

In summary, the conversation discusses the relationship between constriction in a pipe and pressure drop. While the equation P=F/A is typically used to calculate pressure, the Bernoulli equation governs the pressure difference in a pipe with a constriction. The pressure at the constriction is always lower, which drives the air from the inlet to the constriction.
  • #1
frenchy7322
6
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Q: When a person inhales, air moves down the bronchus (windpipe) at 15 cm/s. The average flow speed doubles through a constriction in the bronchus. Assuming incrompressible flow, determine the pressure drop in the constriction.

OK what confuses me is that I thought that if you decrease the width of a passage (e.g cholesterol in an artery) you increase pressure. However this asks for pressure DROP in constriction?:confused:

Equation I thought would be P = F/A, but not real sure at all.

Please help me get the ball rolling!
 
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  • #2
To help you judge, let's compare this.
When there is a constriction in a pipe, the overall pressure in the WHOLE tube should be higher than that of a pipe with no constriction, given similar inlet flow speed. Now look at the tube with constriction, and compare the pressure at the inlet and at the constriction, the pressure at the constriction is always lower. It is this pressure difference that drives the air from inlet to the constriction! That phenomena is governed by the Bernoulli equation.
 

FAQ: Calculating Pressure Drop in a Bronchial Constriction

1. What is pressure drop?

Pressure drop refers to the difference in pressure between two points in a fluid or gas system. In the context of a bronchial constriction, it is the decrease in air pressure as it passes through a narrowed airway or bronchus.

2. How is pressure drop calculated in a bronchial constriction?

The pressure drop in a bronchial constriction can be calculated using the Bernoulli equation, which takes into account the fluid's velocity, density, and the constriction's cross-sectional area. The equation is: ΔP = (ρv2)/2 - (ρv02)/2, where ΔP is the pressure drop, ρ is the density of the fluid, v is the velocity at the constriction, and v0 is the velocity before the constriction.

3. What factors can affect pressure drop in a bronchial constriction?

The main factors that can affect pressure drop in a bronchial constriction are the severity of the constriction, the velocity of the air flow, and the density of the air. Other factors such as the length and shape of the constriction may also play a role.

4. Can pressure drop in a bronchial constriction be harmful?

In general, a certain level of pressure drop in the airways is necessary for proper functioning of the respiratory system. However, excessive pressure drop due to severe constriction can lead to difficulty in breathing and reduced oxygen supply to the body's tissues. This can be harmful, especially for individuals with respiratory conditions such as asthma or chronic obstructive pulmonary disease (COPD).

5. How can pressure drop in a bronchial constriction be managed?

The management of pressure drop in a bronchial constriction depends on the underlying cause. In some cases, medications such as bronchodilators can help relax the airway muscles and reduce pressure drop. In severe cases, surgical intervention may be necessary to widen the constricted airway. Lifestyle changes, such as quitting smoking and avoiding triggers, can also help manage pressure drop in the long term.

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