Why can't a channel flow with two immiscible fluids have two maximum velocities?

In summary, the conversation discusses a 2-D Poiseuille Flow with two immiscible fluids of different densities. The total distance of the channel is L+εL, with the dividing line between the two flows at L. The speaker was initially unsure about the possible flow profiles, but eventually decided to solve the problem. They noticed that the maximum velocities of both fluids always occur at the same height, despite their different ranges. The speaker then asks for an explanation as to why the flow cannot have two maximums, but later understands the reason.
  • #1
member 428835
Hi PF!

I was recently looking at two immiscible fluids in a 2-D Poiseuille Flow with two immiscible fluids of different densities. Let the total distance of the channel be ##L+\epsilon L##, where the dividing line between the two flows is ##L##. I was thinking of the possible flow profiles and finally decided to solve the problem. When I did, I noticed the maximums of the two fluids' velocities always occurred at the same height (keep in mind I'm talking mathematically, as ##v_1 \in [0,L]## and ##v_2 \in [L,\epsilon L]##). The implication being the flow could never have two maximums.

Can someone explain why we cannot have two maximums?
 
Engineering news on Phys.org
  • #2
Nevermind, I understand!
 

1. Why can't a channel flow with two immiscible fluids have two maximum velocities?

This is because the flow is governed by the principle of continuity, which states that the total mass flow rate must remain constant throughout the channel. If there were two maximum velocities, it would violate this principle and lead to an imbalance in the mass flow rate.

2. What is the principle of continuity?

The principle of continuity states that the total mass flow rate must remain constant in a channel flow. This means that as the cross-sectional area of the channel changes, the velocity of the fluid must also change in order to maintain a constant mass flow rate.

3. Can immiscible fluids have different velocities in a channel flow?

No, immiscible fluids cannot have different velocities in a channel flow. This is because they do not mix and therefore cannot have a combined mass flow rate. The principle of continuity requires a single, constant mass flow rate throughout the channel.

4. How does the viscosity of the fluids affect the maximum velocity in a channel flow?

The viscosity of the fluids does not affect the maximum velocity in a channel flow. The maximum velocity is determined by the geometry of the channel and the total mass flow rate, which remains constant regardless of the viscosity of the fluids.

5. Are there any exceptions to the principle of continuity in channel flow?

Yes, there are some exceptions to the principle of continuity. In certain cases, such as when there is a sudden change in the geometry of the channel or when there is a source or sink of fluid, the principle may not hold true. However, in most cases, the principle of continuity remains a fundamental law of fluid mechanics.

Similar threads

Need some intuition for laminar flow in different geometries
    • Mechanical Engineering
Replies
10
Views
2K
Pumping power calculation of a vertical closed-loop system
    • Mechanical Engineering
Replies
4
Views
1K
Fluid Oscillating in a Channel CFD
    • Mechanical Engineering
Replies
12
Views
1K
Horizontal open channel flow -- Hydraulic jump calculation
    • Mechanical Engineering
Replies
1
Views
1K
Bernoulli equation and parallel pipe branch
    • Mechanical Engineering
Replies
31
Views
2K
Predicting flow rates of a pressure driven system
    • Mechanical Engineering
Replies
8
Views
1K
Relationship between volumetric flow rate and pressure
    • Mechanical Engineering
Replies
3
Views
3K
Time to empty gas cylinder (problem worked, but would like feedback)
    • Mechanical Engineering
Replies
7
Views
764
Multiphase Flow in Fluid Dynamics - Energy Coupling
    • Mechanical Engineering
Replies
1
Views
2K
Radiation heat transfer in channel flow
    • General Engineering
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top