# When to use Poiseuille’s Law and when to use the Continuity Equation?

#### nomdeplume1234

##### Full Member
2+ Year Member
If a question does not specify which to use then how do you know which equation is appropriate? For example, it seems that doubling the radius of a pipe would increase the flow speed by 4x if I were using the continuity equation (A1v1 = A2v2) but doubling the radius would increase the flow rate by 16x if I were using Poiseuille's law (Flow = ΔPπr4 / 8Lη).

#### RH8448

##### Full Member
In the question stem or passage, it will guide you whether the use the Continuity or Poiseuille's Equations. Both of them are valuable tools. The Continuity is more simplistic. It applies generally to fluid flow in a tube where viscosity is negligible. But, many other differences occur between the two equations. When it comes to blood vessels in biological organisms, Poiseuille's Equation is able to explain flow better. Because blood is relatively viscous, Pois Eq. is able to show that viscosity is relevant to flow.

So, Continuity says that the larger the diameter the greater the flow. This is very simplistic but true if viscosity is negligible (sort of like with water).

In Pois's Eq. it takes into account that more resistance occurs when the diameter decreases and less resistance occurs when increasing the diameter. This makes sense because when your arteriole blood vessels constrict, your blood pressure increases. Also relevant is the change in pressure. The larger the difference the more flow. Also it accounts for the length of blood vessels. The greater the length, the more resistance, thus less flow.

So, Pois Eq. applies more to biological systems.

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