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Wittaler [7]
3 years ago
8

Determine the Reynolds number for a flow of 0.2 m^3/s through a 203 mm inner diameter circular pipe of a fluid with rho=680 kg/m

^3 ,μ=3.1*10^(-4) ((N-s)/m^2 ),and σ=0.022 N/m.Is the flow laminar or turbulent?
Physics
1 answer:
IrinaK [193]3 years ago
3 0

To find a solution to this problem it is necessary to apply the concepts related to the Reynolds number and its definitions on the type of fluid.

A Reynolds number less than 2000 considers the laminar fluid, while a Reynolds number greater than 4000 is considered a turbulent fluid. (The intermediate between the two values would be a transient fluid)

The mathematical equation that defines the Reynolds number is given by

Re = \frac{\rho V D}{\mu}

Where

\rho = Density

V= Velocity

D= Diameter

\mu = Viscosity

Our values are given as

Q = 0.2m^3/s

D = 203*10^{-3}m

\rho = 680kg/m^3

\mu = 3.1*10^{-4}Ns/m^2

\sigma = 0.022N/m

The velocity can be find through the Discharge equation,

Q = VA

Where

V = Velocity

A = Area

Replacing,

0.2 = V* (2\pi*(\frac{203*10^{-3}}{2})^2)

V = 3.08m/s

Replacing at the Reynolds equation,

Re = \frac{\rho VD}{\mu}

Re = \frac{680*3.08*203*10^{-3}}{3.1*10^{-4}}

Re = 1.37*10^6

Since Reynolds' number is greater than 4000, then we consider this a turbulent fluid.

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The equations for the position and velocity of an object traveling in a straight line is given by the following expressions:

x = x0 + v0 · t + 1/2 · a · t²

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If we place the center of the frame of reference at the point when the bicyclist starts following his friend, the initial position of the bicyclist will be 0, and the initial position of the friend will be his position after 2 s:

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1/2 · a · t² = x0 + v · t       v0 of the bicyclist is 0 because he starts from rest.

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It takes the bicyclist (5.0 s + 2.0 s) 7.0 s to catch his friend after he passes him.

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