Average velocity in a turbulent flow tube

In summary, The conversation discusses the struggle of obtaining the expression for average speed in turbulent flow, and the limitations of the book in explaining the integration process and the undefined logarithmic term. The speaker shares their method of integrating up to a slightly smaller value to achieve a numerical result, but it does not match the equation in the book. The other person suggests checking if there is a missing variable in the equation and asks for the book reference. The first speaker reveals that they have already solved the problem by integrating up to a very close value to R and mentions the book used, which is Bird's Transport Phenomena.
  • #1
Est120
51
3
TL;DR Summary
obtaining the average speed using the logarithmic profile
hi guys
I'm really struggling to get the expression for average speed in turbulent flow

The book explains absolutely nothing about how the integration is carried out, in addition to the fact that the logarithmic term becomes undefined when r = R what I did was carry out the integration up to 0.9999999R in order to obtain a numerical result equal to the one that I could have obtained integrating up to R even so, the expression I got is not the one shown in the book
Turbulent flow- average speed in a flow across a pipe.PNG
 
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  • #2
It would help if you cited the book you are using.

But for starters, are you not missing an ##r## in your denominator to go along with the ##d\theta##?
 
  • #3
boneh3ad said:
It would help if you cited the book you are using.

But for starters, are you not missing an ##r## in your denominator to go along with the ##d\theta##?
i already solved the problem i was supposed to integrate up to 0.9999999999...99999 R (integral in numerator) so i get the equation of the book, the book is Bird's Transport Phenomena
 

Related to Average velocity in a turbulent flow tube

What is average velocity in a turbulent flow tube?

Average velocity in a turbulent flow tube refers to the average speed at which a fluid moves through a tube or channel that is experiencing turbulent flow. This means that the fluid is moving in an irregular and chaotic manner, with fluctuations in velocity and pressure.

How is average velocity calculated in a turbulent flow tube?

The average velocity in a turbulent flow tube is typically calculated by dividing the total volume flow rate by the cross-sectional area of the tube. This gives an overall average velocity for the entire volume of fluid moving through the tube.

What factors affect the average velocity in a turbulent flow tube?

The average velocity in a turbulent flow tube can be affected by a variety of factors, including the diameter and shape of the tube, the viscosity of the fluid, and the overall flow rate. Additionally, any obstructions or changes in the tube's geometry can also impact the average velocity.

Why is average velocity important in turbulent flow?

Average velocity in turbulent flow is important because it helps to determine the overall behavior and characteristics of the fluid moving through the tube. It can also be used to calculate other important parameters, such as the Reynolds number, which is a measure of the fluid's flow regime.

How does average velocity differ from instantaneous velocity in a turbulent flow tube?

Average velocity in a turbulent flow tube is a measure of the overall speed of the fluid over a certain period of time, while instantaneous velocity refers to the speed of the fluid at a specific moment in time. In turbulent flow, the instantaneous velocity can vary greatly, while the average velocity gives a more stable and representative value for the fluid's movement.

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