TABLE 10–3 Coefficients of Viscosity Fluid Coefficient (temperature in °C) of Viscosity, n (Pa·s) Water (0°) 1.8 × 10-3 (20°) (100°) Whole blood (37°) 1.0 × 10-3 0.3 × 10-3 24 × 10-3 Blood plasma (37°) ~1.5 × 10-3 Ethyl alcohol (20°) Engine oil (30°) (SAE 10) Glycerine (20°) Air (20°) Hydrogen (0°) 1.2 × 10-3 200 × 10-3 1500 × 10-3 0.018 × 10¬3 0.009 × 10-3 Water vapor (100°) 0.013 × 10¬3 t1 Pa •s 10 poise (P) = 1000 cP. EXAMPLE 10–12 ESTIMATE Blood flow. In humans, blood flows from the heart into the aorta, from which it passes into the major arteries, Fig. 10–20. |These branch into the small arteries (arterioles), which in turn branch into myriads of tiny capillaries. The blood returns to the heart via the veins. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm/s. A typical capillary has a radius of about 4 x 104 cm, and blood flows through it at a speed of about 5 x 10-m/s. Estimate the number of capillaries that are in the body. APPROACH We assume the density of blood doesn't vary significantly from the aorta to the capillaries. By the equation of continuity, the volume flow rate in the aorta must equal the volume flow rate through all the capillaries. The total area of all the capillaries is given by the area of a typical capillary multiplied by the total number N of capillaries. SOLUTION Let A, be the area of the aorta and A, be the area of all the capil- laries through which blood flows. Then A, = Nurap, where rap = 4 x 104 cm is the estimated average radius of one capillary. From the equation of continuity (Eq. 10-4b), we have v2 A2 vz N rreap Vị A1 Vị Tráorta SO 1.2 × 10-²m 4 x 10-6 m 2 0.40 m/s 5 × 10-4 m/s. Vị raorta 2 7 × 10°, N v2 réap or on the order of 10 billion capillaries.
TABLE 10–3 Coefficients of Viscosity Fluid Coefficient (temperature in °C) of Viscosity, n (Pa·s) Water (0°) 1.8 × 10-3 (20°) (100°) Whole blood (37°) 1.0 × 10-3 0.3 × 10-3 24 × 10-3 Blood plasma (37°) ~1.5 × 10-3 Ethyl alcohol (20°) Engine oil (30°) (SAE 10) Glycerine (20°) Air (20°) Hydrogen (0°) 1.2 × 10-3 200 × 10-3 1500 × 10-3 0.018 × 10¬3 0.009 × 10-3 Water vapor (100°) 0.013 × 10¬3 t1 Pa •s 10 poise (P) = 1000 cP. EXAMPLE 10–12 ESTIMATE Blood flow. In humans, blood flows from the heart into the aorta, from which it passes into the major arteries, Fig. 10–20. |These branch into the small arteries (arterioles), which in turn branch into myriads of tiny capillaries. The blood returns to the heart via the veins. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm/s. A typical capillary has a radius of about 4 x 104 cm, and blood flows through it at a speed of about 5 x 10-m/s. Estimate the number of capillaries that are in the body. APPROACH We assume the density of blood doesn't vary significantly from the aorta to the capillaries. By the equation of continuity, the volume flow rate in the aorta must equal the volume flow rate through all the capillaries. The total area of all the capillaries is given by the area of a typical capillary multiplied by the total number N of capillaries. SOLUTION Let A, be the area of the aorta and A, be the area of all the capil- laries through which blood flows. Then A, = Nurap, where rap = 4 x 104 cm is the estimated average radius of one capillary. From the equation of continuity (Eq. 10-4b), we have v2 A2 vz N rreap Vị A1 Vị Tráorta SO 1.2 × 10-²m 4 x 10-6 m 2 0.40 m/s 5 × 10-4 m/s. Vị raorta 2 7 × 10°, N v2 réap or on the order of 10 billion capillaries.
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