# Q: Solve Poiseuille's Law for Volume Flow Rate

• Nathan phisi
In summary, the conversation is about a large tank containing oil with a viscosity of η = 7.5 Pa s. The tank has walls and floor which are 2 cm thick, and there is a small circular hole at the base of the tank with a radius of 1.5 mm. The fluid pressure at the base of the tank is 126 kPa and the atmospheric pressure is 101 kPa. The question is asking for the volume flow rate of oil leaking out of the tank, with answer choices ranging from 1.2 × 10−3 m3 s −1 to 3.3 × 10−7 m3 s −1. The solution involves using Poiseulle's law equation,
Nathan phisi

## Homework Statement

A large tank contains oil with a viscosity of η = 7.5 Pa s. The tank has walls and floor which are 2 cm thick, but there is a small circular hole at the base of the tank through which oil is leaking. The fluid pressure at the base of the tank is 126 kPa (atmospheric pressure is 101 kPa) and the radius of the hole is 1.5 mm. What is the volume flow rate at which the oil is leaking out of the tank (in m3 s −1 )?

(A) 1.2 × 10−3 (B) 7.1 × 10−4 (C) 2.7 × 10−5 (D) 4.1 × 10−6 (E) 3.3 × 10−7

## Homework Equations

Poiseulle law equation (maybe)

## The Attempt at a Solution

I'm pretty sure this has to do with Poiseulle's law, because of the variables. I have all variables for the P law equation (given in the equation) except length (and the needed flowrate). I do have trouble with 2 variables being unknown, so a little help with that would be greatly appreciated :)

You do know the length.

Nathan phisi
Oh dang, you're right, the length was 0.02m. Don't ask me how long I was on this question and didn't click. Thanks!

## 1. What is Poiseuille's Law?

Poiseuille's Law is a mathematical equation that describes the relationship between fluid flow rate, pressure, and resistance in a cylindrical tube. It was developed by French physicist Jean-Louis-Marie Poiseuille in the 19th century.

## 2. What is the formula for Poiseuille's Law?

The formula for Poiseuille's Law is Q = (πΔP r^4)/(8ηL), where Q is the volume flow rate, ΔP is the pressure difference, r is the radius of the tube, η is the fluid viscosity, and L is the length of the tube.

## 3. What does Poiseuille's Law explain?

Poiseuille's Law explains how the pressure difference between two points in a cylindrical tube affects the volume flow rate of a fluid. It also shows how tube length and radius, as well as fluid viscosity, impact the flow rate.

## 4. How is Poiseuille's Law used in real life?

Poiseuille's Law is used in many practical applications, such as in the design of pipes, blood vessels, and other fluid-carrying systems. It is also used in medical procedures, such as measuring blood flow and administering IV fluids.

## 5. What are some limitations of Poiseuille's Law?

While Poiseuille's Law is a useful equation for describing fluid flow in simple cylindrical tubes, it does not account for more complex factors such as turbulence, irregular tube shapes, and non-Newtonian fluids. Therefore, it may not accurately predict flow in these situations.

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