Flow through a systemic capillary (diameter D = 8 mu m) is driven by pressure gr
ID: 2326521 • Letter: F
Question
Flow through a systemic capillary (diameter D = 8 mu m) is driven by pressure gradient - partial differential P/partial differential z = 7000Pa/cm. The capillary is cylindrical. Blood has viscosity mu = 3.2 centipoise (1 cP = 0.001 Pa-s). There is no need to re-derive the Poiseuille equation developed in class. a. What is the flow rate Q (m^3/s) through the capillary? b. What is the resistance R to flow through the vessel (Pa-s/m^4)? c. What shear stress tau_W does blood apply to the vessel wall (Pa)?Explanation / Answer
Answer a.
Flow rate Q through capillary as per Hagen–Poiseuille equation is = ×R4/8µ×p/z
Here, R = 4 × 10-6 m
µ = 3.2× 0.001 = 3.2 × 10-3 Pa-s
p/z = 7000 pa/cm = 700000 pa/m
Flow rate (Q) = ×(4 × 10-6)4/[8×3.2 × 10-3]×700000
= 2.199 × 10-15 m3/s (Answer)
Answer b.
Resistance to flow through the vessel = µL/R4
Here, µ = 3.2 × 10-3 Pa-s
Length of vessel (L) = Not given
R= 4 × 10-6 m
Resistance= 3.2 × 10-3 × L/ (4 × 10-6)4
= 1.25 × 1019 × L (Answer)
Answer c.
Shear stress applied by blood on the vessel = 32 µ×Q/ ×d3
Here, µ = 3.2 × 10-3 Pa-s
Q = 2.199 × 10-15 m3/s
d= 8 µm = 8×10-6 m
Shear stress applied by blood on the vessel = 32×3.2 × 10-3 × 2.199 × 10-15 / (8×10-6 )3
= 28.15 Pa (Answer)
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