One can inhale the air from ambient by enlarging the lung vo

One can inhale the air from ambient by enlarging the lung volume with energy supplied from the chest muscles. Inhaling through an inlet chamber with small orifice, less air will be suck per unit time with the same chest movement. In order to have the same air flow rate, one needs to inhale deeper. Draw the pressure and velocity distributions from the ambient to the lung (case 1 with no inlet chamber). Draw the pressure and velocity distributions from ambient to the lung (case 2 with inlet chamber). Explain the reason.

Solution

1) According Bernoulli equation we have

Where P is the pressure at a [point in air, v is its velocity,   is its density and h is the height of the point. With every thing else being constant, the distribution of the pressure applied by lungs in inhaling and the resulting velocity of the air (being inhaled) is thus given by

          

where constant .

This equation, when plotted in the graph with v along Y-axis and P along –X axis, gives a parabola

(B) Let the cross sectional area of the ambient be and the cross sectional area of the small orifice in the inlet chamber be . Let the velocities of air in ambient and the inlet chamber be    and respectively. Then according to equation of continuity we have

    (i)

From Bernoulli equation we have

  

Substituting equation (i) into this equation, we get

      

    Or

Which shows that the graph between the distributions of velocity at orifice and the extra pressure exerted by the lungs is a parabola.

(c) The reason of the difference in the distributions in case (A) and case (B) is the consequence of equation of continuity given by eqn. (i) in question (B)