Question

A)The change of fish density is provided by the gas of negligible density in the fish bladder. If fish body density is 1.067 g/cm^3 , calculate the volume of the swim bladder (as percent of the total volume of fish) providing with the average density of 1.024 g/cm^3 .

B)When the rate of blood flow in aorta is 5 Liter/min , the velocity of the blood in capillaries is about 0.3 min/sec .

If the average diameter of capillary is 0.01 mm , calculate how many billions of capillaries in circulatory system.

Answer 1

A)

body density( excluding bladder) = 1.067 g/cm^3

average density of fish inclusive of bladder = 1.024 g/cm^3

average density = 1.024 g/cm^3 = mass of whole body / volume of whole body

= mass of body(leaving out bladder) / ( V1 + V2) V1 = volume of rest of body

V2= volume of bladder

= body density x V1 / ( V1 + V2)

= 1.067 X V1/ ( V1 + V2)

V1+v2/V1 = 1.067 /1.024

V2/v1 = 1.042 - 1 = 0.042

V2(/v1+v2) = 0.042/(1+0.042 ) = 4 %

B) rate of blood flow in aorta = 5lts/mi = 5000 cc/60sec= 250/3 cc/sec = 250/3 X 10^(-6) m3/sec

velocity of blood in capillaries = 0.3 mm/s = 0.3 X 10 ^(-3) m/s

Av diameter of capillaries = 0.01mm ; average radius= 0.005 mm = 0.005 X 10^ (-3) m

no. of capillaries= ?

The governing equation for flow between two piping systems for laminar flow is

n1 X A1 X V1 = n2 X A2 X V2 n1 = 1 aorta n2 = no. of capillaries = ?

A1 = area of aorta ; A2 = area of capillaries V1 = speed of flow in aorta v2 = speed of flow in each capillary

n2 = n1 A1 V1 / A2 V2 = 1 X (250/3) X 10^(-6) m^3/s / ( 3.14 X {0.005 X 10^(-3)}^2 m2 X 0.03 X 10^(-3)m/sec)

Note that A1X V1 = volume of blood flow/sec in aorta

n2 = 3.54 X 10^10 capillaries