Chp 3 Poiseuille's Law: Pressure-Driven Flow Through Tubes

Question 1

Define open circulation? Use an example

Answer 1

Open circulation = ex. blood pumped by a single tubular heart is released into the open field of tissue filling the body, rather than being contained in arteries, capillaries or veins.

Example of an insect

Question 2

Define closed circulation?

Answer 2

Closed circulation = ex. blood is contained in a continuous network of vessels passing through the body.

Question 3

What blood circulatory system do fish have?

Answer 3

Fish have a two-chambered heart, but it is one-sided. Meaning blood expels out of the heart first through the gills to pick up oxygen then to the rest of the tissues, before returning back to the heart via the veins.

Question 4

Describe mammals circulatory system.

Answer 4

Like the fish system, but circulation is divided into 2 segments connected in series. Two-sided heart, each side a pump for its segment of system.

Question 5

Define pulmonary circulation

Answer 5

the right side of the heart sends blood through the lung capillaries at low pressure where the rbc pick up oxygen, before returning to the left side of the heart.

Question 6

Define systemic circulation

Answer 6

Left side of heart pumps returned oxygenated blood to remaining tissues of the body at a much greater pressure.

Question 7

Define cardiac output

Answer 7

volume of blood pumped around system (L/min)

Question 8

Define Poiseuille’s Law

Answer 8

the relationship between fluid flow in a tube and the pressure required to produce this flow.

Question 9

What is Poiseuille’s Law (formula)?

Answer 9

Q = (πa^4 ΔP) / (8μ l)

Q = volume flow rate (m^3/s)
ΔP = pressure difference (Pa, N/m^2, kg/m*s^2) = P1 (fluid in) - P2 (fluid out)
a = tube radius (m)
μ = fluid viscosity (kg/m*s or Pa*s)
l = length over which pressure drop is measured (m)

Question 10

Define Laminar

Answer 10

flow profile, or layered. No-slip condition on walls.

fluid velocity is zero on walls, but increases parabolically toward peak velocity at centerline of tube.

Question 11

Define shear rate

Answer 11

Δu/Δy

layers of fluid sliding past each other.

Question 12

Define shear stress

Answer 12

τ = F/A

it takes a force to overcome the friction of the layers sliding past one another.

Question 13

Define Newtonian

Answer 13

when the viscosity value is a constant that is not dependent upon the flow rate

Question 14

Define Non-Newtonian

Answer 14

fluids viscosity that varies with flow rate.

Question 15

What are the assumptions for Poiseuille’s Law to hold?

Answer 15

1. The length of the tube must be much greater than the radius
2. The flow must be steady in time and laminar in velocity profile
3. The fluid must be Newtonian
4. The tube must be rigid