Biofluid Flow - Principles of Biomedical Engineering - page 117

⎛

V

⎞

1.447

⎛ ⎞

Error 100 * 1

2
1

100 * 1 2.5% = − = − =

⎜ ⎟

⎜ ⎟

V

⎝

1.4843

⎠

⎝ ⎠

4.2.3.1 Analogy with Electrical Circuits
The Poiseuille law corresponds to Ohm's law for electrical circuits. The pressure
difference moves the blood through the system. Similarly, a battery or other power
supply develops a potential difference , which moves electrons around the circuit.
Thus, a fluid pressure drop (energy per unit volume) corresponds to a potential dif-
ference or voltage drop (energy per unit charge). The flow rate of a fluid is analo-
gous to the current in a circuit ( I

t ). From Ohm's law (discussed in Chapter
3), the quantity in parentheses is the resistance. The electrical analog of this fluid
quantity (i.e., the ratio of viscosity to cross sectional area is the resistance) is

= δ q / δ

RLr = ρ

where is the resistivity, L is the length of the conductor, and r is its radius. Ohm's

law is more useful than the Poiseuille law as it is not restricted to long straight wires
with constant current. However, the Poiseuille law is more useful in knowing the
dependency on pipe diameter, pipe length, and liquid viscosity.
In biological systems, many branches stem from a single supply, either in the
circulatory system or in the respiratory system. From the conservation of mass
principle (4.15) the flow into a branch equaled the sum of the flows out. In the elec-
trical case, the same is true for currents at a junction of conductors: conservation
of charge. To find the total resistance in a branched circuitry in series and parallel
configurations, the principles of Kirchoff's law are used. They can also be adapted
to flow systems with the following rules:
When components are in series (Figure 4.3),

ρ

1. The total pressure drop is equal to the sum of the pressure drops across
each component. That is,

Δ=Δ +Δ +Δ PPP P

1 2 3