Math Problem Statement

V/t = pie p r sq4/ 8l n

Solution

It looks like you're trying to express a formula involving the variables VV, tt, π\pi, pp, rr, ll, and nn. Based on your input, I think you might be referring to the Poiseuille's law, which describes the flow of a fluid through a cylindrical pipe.

The correct form of Poiseuille's law is:

Vt=πpr48ηl\frac{V}{t} = \frac{\pi p r^4}{8 \eta l}

Where:

  • V/tV/t represents the volumetric flow rate (QQ).
  • π\pi is a constant (approximately 3.14159).
  • pp is the pressure difference between the two ends of the pipe.
  • rr is the radius of the pipe.
  • η\eta (often written as μ\mu) is the dynamic viscosity of the fluid.
  • ll is the length of the pipe.

It seems like you have a version with a typo where "pie" is used instead of π\pi and "n" instead of η\eta, but the formula is likely aiming to describe fluid flow through a pipe.

Would you like further clarification on this, or is there a specific part of the formula you're looking to solve for?


Follow-up questions:

  1. How is Poiseuille's law used to calculate flow rate in real-world applications?
  2. What are the units for each of these variables in the formula?
  3. How does viscosity η\eta affect the flow rate of a fluid in a pipe?
  4. What happens to the flow rate if the radius of the pipe is doubled?
  5. What is the difference between laminar and turbulent flow in pipes?

Tip:

The flow rate in pipes governed by Poiseuille’s law is highly sensitive to the radius of the pipe, making it a critical factor for understanding fluid dynamics.

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Math Problem Analysis

Mathematical Concepts

Fluid Mechanics
Poiseuille's Law
Algebra

Formulas

V/t = π p r^4 / 8η l

Theorems

Poiseuille's Law

Suitable Grade Level

Grades 11-12