Dear Samuel,

The dimensionelss Reynolds number is generated by the process of making the Navier-Stokes equations (continuity and momentum equations) dimensionless. It is the product of the magnitude of the characteristic velocity by the magnitude of the characteristic length of the problem divide by the kinematic viscosity. Therefore, the Reynolds number cannot be negative. I hope this answers your question.

Best wishes,

Prof. Luca Cortelezzi

McGill University

Hi,

Re cannot be negative. It is a number and a scalar. So, we cannot say velocity direction, etc is affecting its sign.

Dear Samuel,

The dimensionelss Reynolds number is generated by the process of making the Navier-Stokes equations (continuity and momentum equations) dimensionless. It is the product of the magnitude of the characteristic velocity by the magnitude of the characteristic length of the problem divide by the kinematic viscosity. Therefore, the Reynolds number cannot be negative. I hope this answers your question.

Best wishes,

Prof. Luca Cortelezzi

McGill University

hi,

Reynolds number can not be negative in any case because its dimension less number and its shows only magnitude.

Re can not be negative, you must use the absolute value of the velocity to obtain it.

Re is the ratio of inertia forces to viscous forces , so negative makes no sense.

Reynolds number is a dimensionless number ( ratio of viscous stress/ inertial stress) which describes about the nature of the flow: laminar or turbulent. Considering such a quantity as negative have no physical meaning.

The question can and has been analyzed by some as something simple and even a bit naïf, but when we read the work of Luis Brand presented by Clifford Truesdel in Archive for Rational Mechanics and Analysis (1957/58, Volume 1, Issue 1, pp. 35 - 45) "The Pi theorem of dimensional analysis", and early in the second item entitled "Dimensional Matrix", we see the following written statement:

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“We consider problems in which the physical quantities Xi involved have positive measures xi which depend upon a system of m fundamental units U1, U2, . . . . , Um. When these units are changed to….”

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The sentence including "positive mesures xi" placed by a distinguished professor Luis Brand and endorsed by an exponent in Rational Mechanics, Clifford Thruesdel, can lead to some reflection.

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If distance ourselves from the physical sense of dimensionless.numbers and set off for a purely mathematical analysis of the theorem of Pis is needed affirmation that physical quantities must be positive mesures to avoid problems in the deduction.

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Note. Professor Brand wrote the following books: Vectorial Mechanics (1930), Vector and Tensor Analysis (1947), Advanced Calculus (1955), Vector Analysis (1957) and Differential and Difference Equations (1966.)

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I.e. when Brand writes what is transcribed above, or write in the same article that:

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"... The elements of PI are called dimensional quantities, and the numbers are positive regarded as a subclass of PI ...."

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analytically should take into account the signal for the theorem deduction .

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Now physically speaking, dimensionless numbers would make no sense if we considered negative measures, but from this treat as naïf question, is a bit of carelessness on who responds.

the Reynolds number cannot be negative

Reynolds number is a function of fluid properties (density and viscosity), characteristic length and characteristic velocity. The characteristic velocity may be average velocity or magnitude of maximum velocity. All of these parameters (rho, mu, D, V) will always be positive and so there is no possibility of negative Reynolds number.

Dear

Reynolds Number being a dimensionless quantity can not be Negative because it is a ratio of inertial to viscous forces. As friction cannot be negative so Reynolds Number . Further density and length cannot be negative too. Now only velocity is left behind in the formula which can be otherwise . But as we are concerned with only the magnitude of it, thus velocity can not be negative too.

This finally makes Dimensionless Quantity the Re Number only positive number.

Hopes I have explained the querry. Regards

Taimur Ali Shams

I got the negative  value of Reynolds for the 0 (zero) mass flow rate

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