4.) You are working on a bioreactor for culturing a network of cylindrical blood vessels and need to perfuse this network with growth media using pressure driven flow. a.) Calculate the resistance for flow of a fluid with dynamic viscosity of 4 * 10-3 Pa * s at 37°C for the combination of tubes organized as shown to the right, what is the total resistance for the system? You can use units of $\frac{Pa*s}{cm^3}$ and ignore junctional effects. All vessels in a section are the same dimensions. b.) If the pressure drop across the network is 100Pa, what is the flow rate in mL/min? (2x) Radius = 0.5cm Length = 30cm (3x) Radius = 0.2cm Length = 60cm (2x) Radius = 0.5cm Length = 30cm P1 P2
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Step 1: First, calculate the resistance of a single tube using the formula: $R = \frac{8\eta L}{\pi r^4}$, where $\eta$ is the dynamic viscosity, $L$ is the length, and $r$ is the radius. Show more…
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5. Use data on the dimensions of various vessels, which can be found below, to answer the following questions. a. Calculate the pressure drop per cm (for a flow rate of 5 L/min in the aorta), a large artery, an arteriole, and a capillary. Assume that the 5 L/min flow goes through a single vessel. (10 pt) b. Repeat the calculation in part (a), but this time assume the 5 L/min flow goes through an array of vessels in parallel. The number of vessels, N, in the array at each level (large artery, arteriole, and capillary) is the number that is required to have the same total cross-sectional area as the aorta. First calculate N. (10) c. Repeat the calculation in part (a), again assuming that the 5 L/min flow goes through an array of vessels. The number of vessels, N, in the array at each level is the number required to achieve the velocity levels listed in Table 8.3. First calculate/show N (10pt) * For part c, as the velocity for arteriole is not available, find the values only for the rest. The viscosity of blood is 0.035g/cm-s Geometrical properties Structure Diameter (cm) Aorta 1.0 Large arteries 0.3 Main arterial branches 0.1 Terminal branches 0.06 Arterioles 0.002 Capillaries 0.0008 Venules 0.003 Terminal veins 0.15 Main venous branches 0.24 Large veins 0.6 Venae cavae 1.25 Table 8.3 Fluid flow velocities in various systems System v (ÎĽ m/min) Aorta 3.8 x 10^7 (63 cm/s) Large artery 1.2-3.0 x 10^7 (20-50 cm/s) Capillary 3-6 x 10^4 (0.05-0.1 cm/s) Large vein 0.9-1.2 x 10^7 (15-20 cm/s) Vena cava 6.6-9.6 x 10^6 (11-16 cm/s) Mississippi River 1.7 x 10^7 (28 cm/s)
Shaiju T.
Calculate the pressure drop (in mmHg) across the following arterial systems using Poiseuille’s Law with ηblood = 4 x 10^-3 Pa-s, for a total flow of 80 cm^3/s across each system; (1 Pa = 0.0075 mmHg). a. aorta (internal radius r = 1.30 cm, length L = 11 cm, all of the flow in this one aorta) b. large arteries (r = 0.3 cm, L = 80 cm, n = 200 of them, each with equal flow and the same dimensions) c. arterioles (r = 35 μm, L = 0.8 cm, n = 5 x 10^5) d. capillaries (r = 3.8 μm, L = 3 mm, n = 10^10)
Adi S.
Using Poiseuille's Law, calculate the pressure drop across the following arterial systems with η blood = 4 x 10^-3 Pa-s, for a total flow of 80 cm^3/s across each system; (1 Pa = 0.0075 mmHg). EXPRESS YOUR ANSWER IN mmHg 1. aorta (internal radius r = 1.30 cm, length L = 11 cm, all of the flow in this one aorta) 2. large arteries (r = 0.3 cm, L = 80 cm, n = 200 of them, each with equal flow and the same dimensions) 3. arterioles (r = 35 μm, L = 0.8 cm, n = 5 x 10^5) 4. capillaries (r = 3.8 μm, L = 3 mm, n = 10^10)
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