Problem 45413. Characterize fluid flow in a pipe as to laminar or turbulent

Created by Karl Ezra Pilario

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In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.Hence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, Re. For a fluid flowing inside a circular pipe, Re is computed as follows:<pre class="language-matlab">Re = D x v x rho / mu
 where:
 D = inside diameter of the pipe [m]
 v = mean flow velocity [m/s]
 rho = fluid density [kg/m^3]
 mu = fluid viscosity [Pa.s] or [kg/m/s]
</pre>Note: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.We can then adopt the following rule: If Re &lt; 2300, the flow is laminar; if Re &gt; 2900, the flow is turbulent; otherwise, the flow is in transition.Write a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of <tt>D</tt>, <tt>v</tt>, <tt>rho</tt>, and <tt>mu</tt> in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.See sample test cases:<pre class="language-matlab">&gt;&gt; flow_pattern([0.02 0.1 1000 8.9e-4])
ans =
 'LAMINAR'
&gt;&gt; flow_pattern([0.02 0.5 1000 8.9e-4])
ans =
 'TURBULENT'
&gt;&gt; flow_pattern([0.02 0.1 1200 8.9e-4])
ans =
 'TRANSITION'
</pre>

In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.

Hence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, *Re*. For a fluid flowing inside a circular pipe, *Re* is computed as follows:

Re = D x v x rho / mu
    where:
    D = inside diameter of the pipe [m]
    v = mean flow velocity [m/s]
    rho = fluid density [kg/m^3]
    mu = fluid viscosity [Pa.s] or [kg/m/s]
 
Note: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.

We can then adopt the following rule: If *Re* < 2300, the flow is laminar; if *Re* > 2900, the flow is turbulent; otherwise, the flow is in transition.

Write a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of |D|, |v|, |rho|, and |mu| in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.

See sample test cases:

>> flow_pattern([0.02 0.1 1000 8.9e-4])
ans =
    'LAMINAR'
>> flow_pattern([0.02 0.5 1000 8.9e-4])
ans =
    'TURBULENT'
>> flow_pattern([0.02 0.1 1200 8.9e-4])
ans =
    'TRANSITION'

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Problem 45413. Characterize fluid flow in a pipe as to laminar or turbulent

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