The average velocity of blood flow in the aorta in a resting man is 20cm/s. The

Question

The average velocity of blood flow in the aorta in a resting man is 20cm/s. The radius of the aorta is 1.2cm. At rest, the number of opened capillaries is about n=12*109. They have an average length of 1=0.75mm and a radius r=3 mu m. What is the blood flow velocity in the capillaries? What time does a red blood cell spend in a capillary on average? What is the total area of all the capillary walls? Compare this with the total surface area of all the red blood cells (erythrocytes). Consider that, as an approximation, an erythrocyte has a discoidal form with radius R=4 mu m and width d=2 mu m. The concentration of erythrocytes is about c=5*106/mm3, and the average blood volume V=5L.

Explanation / Answer

Averagevelocity of the blood flow v = 20 cm / s = 0.2 m/ s Radius of aorta r = 1.2 cm = 0.012 m No.of opened capillaries N = 12*10^9 Average length L =0.75 mm = 0.75*10^-3 m Average raius of capillary r ' = 3 * 10 ^ -6m Area of cross section of aorta A = r^ 2                                                  = 4.523 * 10 ^ -4 m ^ 2 Voloume flow rate V = Av = 9.046 * 10 ^ -5 m ^3 /s Area of cross section of capillary A ' =r'^2                                                         = 2.827 * 10 ^ -11 m ^ 2 from equation fo continuity   Av = NA'v ' blood flow in capillary v ' = Av / N A'                                        = V / NA'                                        = 2.666 *10^-4 m / s (b). required time t = length / v '                              = L / v '                             = 2.812 s (c). Total area of the capillary wall = r ' ^ 2L                                                      =2.12*10 ^ -14 m ^ 3                                  

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