Solving Non-Steady Flow of Newtonian Fluid in Circular Pipe

In summary: This equation can then be solved using iterative methods such as the Gauss-Seidel method or the Successive Over-Relaxation method. In summary, the problem is to find the velocity distribution for a non-steady flow of a Newtonian fluid in a circular pipe. Starting with the mass and momentum balance equations, the equation for dp/ds is obtained. By assuming the solution is separable, the simplified equation can be solved using finite difference methods. The final equation can be written as a difference equation and solved iteratively for the value of p at various positions.
  • #1
lohanlotter
7
0
I am to find the velocity distribution where there is non steady flow of a Newtonian fluid in a circular pipe. I did a mass and momentum balance around the system and ended up with the following equation:
dp/ds = 4 + 1/e*d/de(e*dp/de)

The derivatives in the equation are partial derivatives

the values of p,s,e are dimensionless numbers.

I am to assume that the solution is separable and then use finite difference method to solve for p. This is where i am having problems. What will the equation be after the assumption is made and the equation is simplified.

I have attempted the question:

I equated the right hand side = 0:

4 + 1/e*d/de(e*dp/de) = 0

and made the partial derivatives total derivatives and then applied the chain rule:

4 + 1/e*dp/de + d/de(dp/de). Is this correct?
 
Physics news on Phys.org
  • #2
Assuming the solution is separable, this equation simplifies to:dp/de + d/de(dp/de) = -4/eThis equation can be solved using finite difference methods. The equation can be rewritten as a difference equation in which the unknown is p. The equation can be written in the form:p_i+1 - 2p_i + p_i-1 = -4/e * dx^2
 

1. What is non-steady flow in a circular pipe?

Non-steady flow refers to the movement of a fluid in a circular pipe that is constantly changing and is not in a state of equilibrium. This can occur when there are changes in the flow rate, pressure, or velocity of the fluid.

2. How is non-steady flow different from steady flow?

In steady flow, the properties of the fluid, such as velocity and pressure, remain constant over time. Non-steady flow, on the other hand, involves changes in these properties over time, making it more complex to analyze and solve.

3. What is a Newtonian fluid?

A Newtonian fluid is a type of fluid that follows Newton's law of viscosity, which states that the shear stress in a fluid is directly proportional to the velocity gradient. This means that the viscosity of a Newtonian fluid remains constant regardless of the applied shear stress.

4. How is non-steady flow of a Newtonian fluid in a circular pipe solved?

The non-steady flow of a Newtonian fluid in a circular pipe can be solved using the Navier-Stokes equations, which describe the conservation of mass and momentum in a fluid. These equations can be solved analytically or numerically using computational methods.

5. What factors can affect the non-steady flow of a Newtonian fluid in a circular pipe?

The non-steady flow of a Newtonian fluid in a circular pipe can be affected by various factors, such as changes in flow rate, pressure, temperature, and fluid properties. The geometry and roughness of the pipe also play a role in the flow behavior. Additionally, any external forces or obstacles can also impact the non-steady flow of the fluid.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
15
Views
2K
Replies
19
Views
953
Replies
18
Views
920
  • Classical Physics
Replies
6
Views
139
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
772
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
6K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Back
Top