Which equation would you use when you were describing a flowing viscous fluid?
Select one:
a. The Bernouilli Equation
b. The Poiseuille Equation
c. The equation of continuity
d. And of the Equation of continuity or the Bernouilli Equation or the Poiseuille Equation.
When describing a flowing viscous fluid, the equation typically used is the Poiseuille Equation, which relates the flow rate of a fluid through a pipe to the viscosity of the fluid, the pressure difference across the pipe, and the dimensions of the pipe.
To arrive at this equation, we consider a steady, laminar flow in a cylindrical pipe, assuming the fluid is incompressible and its flow is fully developed (meaning that the fluid velocity does not change along the length of the pipe).
The Poiseuille Equation is given by:
Q = (π * ΔP * r^4) / (8 * η * L)
where:
- Q represents the volumetric flow rate (in m^3/s),
- ΔP represents the pressure difference (in Pa),
- r represents the radius of the pipe (in m),
- η represents the dynamic viscosity of the fluid (in Pa.s), and
- L represents the length of the pipe (in m).
So, in this case, the correct answer would be (b) the Poiseuille Equation.