Flow Through Tubes

Question 1

Define Pressure (P)

Answer 1

Force exerted per unit area (surface area)

Question 2

Define Pressure Gradient (∆P)

Answer 2

Difference in forces exerted (per unit area) at either end/side of an object

Question 3

Define Flow (Q)

Answer 3

The volume of liquid passing a given level of the circulation/airways per unit time

Question 4

Define Resistance

Answer 4

A force that tends to oppose the flow of a substance

Question 5

Define Velocity

Answer 5

The rate of movement of fluid particles along a vessel/airway

Question 6

Define viscosity

Answer 6

The property of resistance to flow in a fluid or semifluid

Question 7

How is a pressure gradient calculated? How can this be applied clinically?

Answer 7

∆P=QR (BP= CO x SVR)

Question 8

What is the relationship between flow and pressure gradient?

Answer 8

Flow is directly proportional to pressure gradient assuming all other things are equal

Question 9

Describe the relationship between resistance and radius if the flow is constant in laminar flow.

What is the clinical application of this?

Answer 9

Laminar flow means that the resistance is greatly affected by the radius of the tube (if flow is constant)

Narrowing of vessels/valves or airways means that the pressure gradient (i.e. blood pressure) has to be greatly increased to maintain constant flow. The velocity will also be increased, causing a wheeze in airways or bruits in blood vessels.

Question 10

What affects resistance? Give a clinical example

Answer 10

Resistance depends on the radius of the vessel/airway and the viscosity of the fluid

E.g. Bronchoconstriction in asthma, reduced flow of air entry.

Question 11

How is flow (Q) calculated? (Laminar flow)

What is the result of this?

Answer 11

Flow = pressure gradient/ resistance

(resistance= 8nl/πr⁴)

Q=∆Pπr⁴

8nl

Flow is directly proportional to r^4​

• Radius doubled: flow increases 16 times
• Radius halved: flow decreases 16 times

Question 12

Describe the relationship between flow, velocity and cross sectional area of the circulation/airways if the flow is constant.

Answer 12

If the flow is constant, velocity is inversely proportional to the cross-sectional area (V=Q/A) (A=𝜋𝑟2) (decrease in area= increase in velocity)

Question 13

What is laminar flow?

Answer 13

Fluid moves in organised layers through tube. Velocity will be highest in the centre of the tube and lowest at the outer edges.

Question 14

Describe the relationship between flow, velocity and cross sectional area if the pressure gradient (not the flow) is constant (in laminar flow)

Answer 14

If the pressure gradient is constant, a reduction in cross sectional area results in decreased velocity in laminar flow and a decrease in flow due to increased resistance from smaller vessel.

Question 15

What is Pouiselle’s Law?

Answer 15

The resistance of the vessel depends on its radius, its length and the viscosity of the fluid:

Resistance = 8nl/πr⁴

n=viscosity

l=length

r=radius

Question 16

What would happen to the velocity and pressure gradient if the radius of a tube was halved and the flow is kept constant?

Answer 16

Velocity would increase x4

Pressure gradient would increase x16

Question 17

What would happen to the velocity and flow if the radius of a tube was halved and the pressure gradient was kept constant?

Answer 17

Velocity would reduce x4

Flow would reduce x16

Question 18

What is turbulent flow?

What are the consequences of this clinically?

Answer 18

Breaking up of layers of laminar flow causing flow to become disordered.

Turbulent flow means greater resistance, can result in damage to the endothelium of blood vessels

Question 19

What makes flow more likely to be turbulent?

Answer 19

Increased velocity (from narrowed vessel)

Low viscosity (less adhesion between layers)

High blood vessel diameter (difficult for layers to maintain ordered flow)

Question 20

What is the effect of branching of the circulation on resistance?

Answer 20

Resistances combine in vessels that are in parallel rather than in series; the overall resistance is reduced.

The flow through each vessel/airway will be inversely proportional to its resistance.

(Arterioles have the highest resistance as they are arranged more in series)

Question 21

What happens if the resistance of resistance vessels (small arteries and arterioles) increases?

Answer 21

The heart must increase the pressure gradient by increasing stroke work to maintain cardiac output

Question 22

What is transmural pressure?

Answer 22

Transmural pressure = intravascular pressure - extravascular pressure.

Transmural pressure has to be >0 in order to keep blood vessels open

Question 23

What is the effect of resistance from increasing pressure in blood vessels?

Answer 23

Increased pressure causes decrease in resistance in blood vessels as they are distensible rather than rigid. Therefore increased pressure causes an increase in radius which reduces resistance.

Question 24

What is the advantage of distensibility of blood vessels?

Answer 24

Distensibility of blood vessels gives them capacitance, allowing them to store blood.