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Rayleigh number based on length for annular space between concentric cylinders Formula

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Rayleigh Number is a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences of temperature and density at the top and bottom. Check FAQs

Ra l = \frac{Ra c}{\frac{({(\ln (\frac{d o}{d i}))}^{4})}{(L^{3}) \cdot {(({d i}^{- 0.6}) + ({d o}^{- 0.6}))}^{5}}}

Ra_l - Rayleigh Number?Ra_c - Rayleigh Number(t)?d_o - Outer Diameter?d_i - Inner Diameter?L - Length?

Rayleigh number based on length for annular space between concentric cylinders Example

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Here is how the Rayleigh number based on length for annular space between concentric cylinders equation looks like with Values.

Here is how the Rayleigh number based on length for annular space between concentric cylinders equation looks like with Units.

Here is how the Rayleigh number based on length for annular space between concentric cylinders equation looks like.

0.258 = \frac{0.075}{\frac{({(\ln (\frac{0.26}{35}))}^{4})}{(3^{3}) \cdot {((35^{- 0.6}) + ({0.26}^{- 0.6}))}^{5}}}

0.258 = \frac{0.075}{\frac{({(\ln (\frac{0.26m}{35m}))}^{4})}{({3m}^{3}) \cdot {(({35m}^{- 0.6}) + ({0.26m}^{- 0.6}))}^{5}}}

0.258 = \frac{0.075}{\frac{({(\ln (\frac{0.26}{35}))}^{4})}{(3^{3}) \cdot {((35^{- 0.6}) + ({0.26}^{- 0.6}))}^{5}}}

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Rayleigh number based on length for annular space between concentric cylinders Solution

Follow our step by step solution on how to calculate Rayleigh number based on length for annular space between concentric cylinders?

FIRST Step Consider the formula

Ra l = \frac{Ra c}{\frac{({(\ln (\frac{d o}{d i}))}^{4})}{(L^{3}) \cdot {(({d i}^{- 0.6}) + ({d o}^{- 0.6}))}^{5}}}

Next Step Substitute values of Variables

∴

Ra l = \frac{0.075}{\frac{({(\ln (\frac{0.26m}{35m}))}^{4})}{({3m}^{3}) \cdot {(({35m}^{- 0.6}) + ({0.26m}^{- 0.6}))}^{5}}}

Next Step Prepare to Evaluate

∴

Ra l = \frac{0.075}{\frac{({(\ln (\frac{0.26}{35}))}^{4})}{(3^{3}) \cdot {((35^{- 0.6}) + ({0.26}^{- 0.6}))}^{5}}}

Next Step Evaluate

∴

Ra l = 0.257969846917731

LAST Step Rounding Answer

∴

Ra l = 0.258

Rayleigh number based on length for annular space between concentric cylinders Formula Elements

Variables

Functions

Rayleigh Number

Rayleigh Number is a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences of temperature and density at the top and bottom.

Symbol: Ra_l

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Rayleigh Number

Rayleigh Number(t)

Rayleigh Number(t) is a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences of temperature and density at the top and bottom.

Symbol: Ra_c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Rayleigh Number(t)

Outer Diameter

The Outer Diameter is the diameter of outer edge of circular hollow shaft.

Symbol: d_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Diameter

Inner Diameter

The Inner Diameter is the diameter of inner circle of circular hollow shaft.

Symbol: d_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Diameter

Length

Length is the measurement or extent of something from end to end.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Rayleigh and Reynolds Number category

Go Rayleigh number based on turbulence for annular space between concentric cylinders

Ra c = (\frac{({(\ln (\frac{d o}{d i}))}^{4}) \cdot (Ra l)}{(L^{3}) \cdot {(({d i}^{- 0.6}) + ({d o}^{- 0.6}))}^{5}})

Go Rayleigh number based on turbulence for concentric spheres

Ra c = {(\frac{L \cdot Ra l}{({(D i \cdot D o)}^{4}) \cdot ({(({D i}^{- 1.4}) + ({D o}^{- 1.4}))}^{5})})}^{0.25}

Go Reynolds Number given Graetz Number

Re L = Gr \cdot \frac{L}{Pr \cdot D}

Go Reynolds Number given Rotational Speed

Rew = w \cdot π \cdot \frac{D^{2}}{v k}

How to Evaluate Rayleigh number based on length for annular space between concentric cylinders?

Rayleigh number based on length for annular space between concentric cylinders evaluator uses Rayleigh Number = Rayleigh Number(t)/((((ln(Outer Diameter/Inner Diameter))^4))/((Length^3)*((Inner Diameter^-0.6)+(Outer Diameter^-0.6))^5)) to evaluate the Rayleigh Number, The Rayleigh number based on length for annular space between concentric cylinders formula is defined as a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences in temperature and density at the top and bottom. Rayleigh Number is denoted by Ra_l symbol.

How to evaluate Rayleigh number based on length for annular space between concentric cylinders using this online evaluator? To use this online evaluator for Rayleigh number based on length for annular space between concentric cylinders, enter Rayleigh Number(t) (Ra_c), Outer Diameter (d_o), Inner Diameter (d_i) & Length (L) and hit the calculate button.

FAQs on Rayleigh number based on length for annular space between concentric cylinders

What is the formula to find Rayleigh number based on length for annular space between concentric cylinders?

The formula of Rayleigh number based on length for annular space between concentric cylinders is expressed as Rayleigh Number = Rayleigh Number(t)/((((ln(Outer Diameter/Inner Diameter))^4))/((Length^3)*((Inner Diameter^-0.6)+(Outer Diameter^-0.6))^5)). Here is an example- 2.063759 = 0.075/((((ln(0.26/35))^4))/((3^3)*((35^-0.6)+(0.26^-0.6))^5)).

How to calculate Rayleigh number based on length for annular space between concentric cylinders?

With Rayleigh Number(t) (Ra_c), Outer Diameter (d_o), Inner Diameter (d_i) & Length (L) we can find Rayleigh number based on length for annular space between concentric cylinders using the formula - Rayleigh Number = Rayleigh Number(t)/((((ln(Outer Diameter/Inner Diameter))^4))/((Length^3)*((Inner Diameter^-0.6)+(Outer Diameter^-0.6))^5)). This formula also uses Natural Logarithm (ln) function(s).

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Rayleigh number based on length for annular space between concentric cylinders Formula

Rayleigh number based on length for annular space between concentric cylinders Example

Rayleigh number based on length for annular space between concentric cylinders Solution

Rayleigh number based on length for annular space between concentric cylinders Formula Elements

Other formulas in Rayleigh and Reynolds Number category

How to Evaluate Rayleigh number based on length for annular space between concentric cylinders?

FAQs on Rayleigh number based on length for annular space between concentric cylinders

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