Solving Poiseuille's Law Trouble - Flow Rate Calculation

In summary, Poiseuille's Law is a mathematical equation used to calculate the flow rate of a fluid through a cylindrical pipe. It takes into account factors such as viscosity, pipe dimensions, and pressure difference. The equation for calculating flow rate is Q = (π * r^4 * ΔP) / (8 * η * L) and the units of measurement will vary depending on the units used for each variable. Some real-life applications of Poiseuille's Law include designing pipes for fluid transportation and medical procedures. However, factors such as turbulence, irregularities in pipe shape, and changes in temperature or pressure can affect its accuracy in real-life scenarios.
  • #1
rddimtbo
3
0
Trouble with a problem. What is the flow rate if a tube consists of two sections, the first with a length of 20cm and radius 0.15cm and the second part with length 1.0cm radius 0.05? with a pressure difference across the entire tube of 3cmHg (p1-p3). (viscosity = 0.801 cP)

I've tried this and end up with two many unknowns and not enough equations. Can anybody help?
 
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  • #2
[tex]\dot V = \frac{\pi \, r_1^4}{8\,\eta}\frac{p_3-p_2}{l_{32}}[/tex]
[tex]\dot V = \frac{\pi \, r_2^4}{8\,\eta}\frac{p_2-p_1}{l_{21}}[/tex]
Well, just solve this for p2 und dV/dt and you have your result :)
 

FAQ: Solving Poiseuille's Law Trouble - Flow Rate Calculation

What is Poiseuille's Law?

Poiseuille's Law is a mathematical equation that describes the flow rate of a fluid through a cylindrical pipe. It takes into account factors such as the fluid's viscosity, the dimensions of the pipe, and the pressure difference between the two ends of the pipe.

How do you calculate flow rate using Poiseuille's Law?

The equation for calculating flow rate using Poiseuille's Law is Q = (π * r^4 * ΔP) / (8 * η * L), where Q is the flow rate, r is the radius of the pipe, ΔP is the pressure difference, η is the fluid's viscosity, and L is the length of the pipe. It is important to use consistent units (e.g. meters for length and pascals for pressure) in order to get an accurate result.

What are the units of measurement for Poiseuille's Law?

The units of measurement for Poiseuille's Law will depend on the units used for each variable in the equation. Generally, Q will be measured in cubic meters per second (m^3/s), r will be measured in meters (m), ΔP will be measured in pascals (Pa), η will be measured in pascal-seconds (Pa*s), and L will be measured in meters (m).

What are some real-life applications of Poiseuille's Law?

Poiseuille's Law has many real-life applications, such as in the design of pipes and tubing for fluid transportation, medical procedures such as blood flow through veins and arteries, and industrial processes involving the flow of liquids or gases through narrow channels.

What factors can affect the accuracy of Poiseuille's Law in real-life scenarios?

While Poiseuille's Law is a useful tool for calculating flow rate, it may not always accurately reflect real-life scenarios due to factors such as turbulence in the fluid, irregularities in the shape of the pipe, and changes in temperature or pressure. In these cases, more complex models or experimental data may be necessary for accurate calculations.

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