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The flow of a liquid in a 2 inch nominal diameter steel pipe produces a pressure drop due to friction of 78.86 kPa. The length of pipe is 40 m and the mean velocity is 3 m/s. if the density of the liquid is 1000 kg/m^3, then a) determine the reynolds number b) determind if the flow is laminar or tubulent c) compute viscosity of the liquid d) compute the mass flow rate (assume ?, equivalent roughness factor, for Steel pipe to be 45.7 x 10-6 m)

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Answer:

Explanation:

The detailed steps and careful analysis is as shown in the attached file.

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Based on the calculations, the Reynolds number is equal to [tex]2.9 \times 10^3[/tex]

Given the following data:

  • Length of pipe = 40 meters.
  • Diameter of pipe = 2 inches to m = 0.0508 m.
  • Pressure drop = 78.86 kPa.
  • Mean velocity = 3 m/s.
  • Density of liquid = 1000 [tex]kg/m^3[/tex].
  • Roughness factor = [tex]45.7 \times 10^{-6}[/tex] m.

How to calculate the Reynolds number.

Reynolds number has a direct relationship with friction factor. Thus, we would determine the friction factor by using this formula:

[tex]f=\frac{2 \Delta P D}{ \rho Lu^2}[/tex]

Where:

  • D is the diameter.
  • L is the length.
  • [tex]\Delta P[/tex][tex]\DeltaP[/tex][tex]\DeltaP[/tex] is the pressure drop.
  • u is the mean velocity.
  • [tex]\rho[/tex] is the density.

Substituting the given parameters into the formula, we have;

[tex]f=\frac{2 \times 78.86 \times 10^3 \times 0.0508}{ 1000 \times 40 \times 3^2}\\\\f=\frac{8012.176}{360000}[/tex]

f = 0.0223.

For the Reynolds number:

[tex]N_{Re}=\frac{64}{f} \\\\N_{Re}=\frac{64}{0.0223}[/tex]

Reynolds number = [tex]2.9 \times 10^3[/tex]

Note: Fluid flow is turbulent when Reynolds number is greater than 2000 ([tex]N_{Re} > 2000[/tex]) and it is laminar when it is lesser than 2000 ([tex]N_{Re} < 2000[/tex]).

b. The flow of this liquid is turbulent.

c. To determine the viscosity:

[tex]V=\frac{\rho uD}{N_{Re}} \\\\V=\frac{1000 \times 3 \times 0.0508}{2.9 \times 10^3} \\\\V=\frac{152.4}{2.9 \times 10^3}[/tex]

V = 0.0526 Kgm/s.

d. To determine the mass flow rate:

[tex]m=\rho A u=\rho u\frac{\pi}{4} D^2\\\\m=1000 \times 3 \times 0.7854 \times 0.0508^2[/tex]

m = 6.081 Kg/s.

Read more on Reynolds number here: https://brainly.com/question/14306776

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