Viscous fluid moving in a pipe

In summary, the conversation is discussing a problem related to hydrodynamics and Hagen-Poiseuille's law. The problem involves a viscous fluid moving through a pipe at a flow rate of 2 x 10^-3 m3/s. The solution involves using the formula for Hagen-Poiseuille's law to calculate the flow in a new pipe with different dimensions and pressure difference. The conversation also mentions the intention of the lecture and the difficulty of the problem.
  • #1
mary d
A viscous fluid is moving through a pipe. The flow is 2 x 10^-3 m3/s
then you have a second tube with a fluid with twice the viscosity which is moving in a pipe whose length is 3 times the original with a radius 1.5 times the original. The pressure difference across this new pipe is 1/3 that of the original. What is the flow in the new pipe?
Again I have no idea where to start. What is the formula? I wonder if anyone could figure out how fast my professor could travel down that pipe of course using the same diameter? Sorry I just had to say it. Thanks for any help!
 
Physics news on Phys.org
  • #2
mary d,
maybe I'm mistaken but it seems to me that this lecture goes thru hydrodnamics at a very quick pace, deriving some formulae for practical use by engineers or scientists. It looks to me like the lecture's intention is not a profound understanding of physical principles, but rather to give the students a 'toolbox' for further use. Please correct me if I'm wrong.

This problem looks like an exercise in Hagen-Poiseuille's law, which states

dp/dz = -8 eta R-2 v

where
z is horizontal position along pipe,
p is pressure at position z,
eta is viscosity of liquid,
R is radius of round pipe,
v is mean velocity of liquid.
 
  • #3


To calculate the flow in the new pipe, we can use the equation for volumetric flow rate, Q = (πr^4ΔP)/(8μL), where Q is the flow rate, r is the radius, ΔP is the pressure difference, μ is the viscosity, and L is the length of the pipe.

Since we know the flow rate and viscosity of the original pipe, we can set up a ratio between the two pipes: (Q1/μ1) = (Q2/μ2). We can then rearrange the equation to solve for Q2, the flow rate in the new pipe.

Q2 = (Q1 x μ2)/μ1

We also know that the length of the new pipe is 3 times longer and the radius is 1.5 times larger than the original pipe. So, we can substitute these values into the equation and solve for Q2:

Q2 = (2 x 10^-3 m^3/s x 2μ1)/(μ1 x 1.5^4)

Q2 = 0.53 x 10^-3 m^3/s

Therefore, the flow rate in the new pipe is approximately 0.53 x 10^-3 m^3/s.

As for the professor traveling down the pipe, it would depend on the velocity of the fluid, which is not given in the problem. However, it is safe to assume that the professor would be able to travel faster in the new pipe due to the higher viscosity and smaller pressure difference.
 

What factors affect the flow of a viscous fluid in a pipe?

The flow of a viscous fluid in a pipe is affected by several factors, including the fluid's viscosity, the pipe's diameter, the pressure difference between the two ends of the pipe, and the length and roughness of the pipe. These factors can influence the speed and stability of the flow.

Why is it important to study the flow of viscous fluids in pipes?

The study of viscous fluid flow in pipes is important for several reasons. Firstly, it helps engineers design efficient pipe systems for different applications, such as in chemical processing, oil and gas transportation, and water distribution. Secondly, understanding the flow behavior can help predict potential issues, such as clogging or erosion, and prevent them from occurring. Additionally, studying the flow of viscous fluids can also provide insights into larger-scale fluid dynamics and phenomena.

What is the difference between laminar and turbulent flow in a pipe?

Laminar flow occurs when the fluid particles move in parallel layers with minimal mixing, resulting in a smooth and orderly flow. In contrast, turbulent flow is characterized by chaotic and random motion of fluid particles, resulting in mixing and eddies. The transition from laminar to turbulent flow is determined by the fluid's velocity, viscosity, and the pipe's geometry.

How does the viscosity of a fluid affect its flow in a pipe?

The viscosity of a fluid plays a crucial role in determining the flow behavior in a pipe. Viscosity is a measure of a fluid's resistance to flow, and highly viscous fluids have a higher resistance than low-viscosity fluids. This means that highly viscous fluids will flow slower and with more stability compared to low-viscosity fluids. The viscosity of a fluid can also change with temperature and pressure, which can affect the flow behavior in a pipe.

What are some common methods used to measure the flow of viscous fluids in pipes?

There are several methods used to measure the flow of viscous fluids in pipes, including flow meters, pressure drop measurements, and velocity profile measurements. Flow meters, such as electromagnetic or ultrasonic flow meters, measure the volume or mass flow rate of the fluid. Pressure drop measurements involve measuring the pressure difference between two points in the pipe to determine the flow rate. Velocity profile measurements use techniques like laser Doppler anemometry or hot-wire anemometry to measure the velocity of the fluid at different points in the pipe, allowing for the calculation of the flow rate.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
908
Replies
19
Views
955
  • Introductory Physics Homework Help
Replies
1
Views
909
  • Introductory Physics Homework Help
2
Replies
43
Views
2K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Mechanical Engineering
Replies
4
Views
731
  • General Engineering
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Replies
18
Views
921
Back
Top