Poiseuille's law states that the resistance R for blood...

Poiseuille's law states that the resistance $R$ for blood flowing in a blood vessel varies directly as the length $L$ of the vessel and inversely as the fourth power of its radius $r$. Stated as an equation, $$ R(L, r)=k \frac{L}{r^{4}} \quad k \text { a constant } $$ Find $R_{L}(4,0.2)$ and $R_{r}(4,0.2),$ and interpret the results.

Poiseuille's law states that the resistance $R$ for blood flowing in a blood vessel varies directly as the length $L$ of the vessel and inversely as the fourth power of its radius $r$. Stated as an equation,
$$
R(L, r)=k \frac{L}{r^{4}} \quad k \text { a constant }
$$
Find $R_{L}(4,0.2)$ and $R_{r}(4,0.2),$ and interpret the results.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Partial Derivatives

Partial derivatives are tools used in multivariable calculus to determine the rate at which a function changes with respect to one variable while keeping the other variables constant. They provide insight into how each individual variable influences the overall behavior of the function.

Sensitivity Analysis

Sensitivity analysis involves examining the changes in a function's output as one or more inputs are varied. By computing partial derivatives, one can assess how sensitive the function is to changes in each independent variable, which is crucial for understanding and predicting the behavior of complex systems.

Direct and Inverse Variation

Direct and inverse variation describe relationships where a change in one variable produces a proportional change in another, either in the same direction or in the opposite direction. Recognizing these relationships is essential for modeling and interpreting phenomena in which variables are interdependent, highlighting how increases in one variable can either boost or dampen the value of the function.

Transcript

Please give Ace some feedback