Calculate the Reynolds number for the flow of oil in a pipe and determine if it is laminar or turbulent.

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ScanSolve AI Tutor · Accepted Answer

To determine whether the flow is laminar or turbulent, we need to calculate the Reynolds number ( $Re$ ).

Identify the given values and convert units.
Specific gravity of oil ( $\text{SG}$ ) = 0.9
Dynamic viscosity of oil ( $\mu$ ) = $47.9 \times 10^{-3} \, \text{Ns/m}^2$ (assuming Ns/m³ is a typo and should be Ns/m²)
Pipe diameter ( $D$ ) = $152 \, \text{mm} = 0.152 \, \text{m}$
Velocity of flow ( $V$ ) = $0.60 \, \text{m/s}$
Density of water ( $\rho_{\text{water}}$ ) = $1000 \, \text{kg/m}^3$
Calculate the density of the oil ( $\rho_{\text{oil}}$ ).
The specific gravity is the ratio of the fluid's density to the density of water.
$\rho_{\text{oil}} = \text{SG} \times \rho_{\text{water}}$ $\rho_{\text{oil}} = 0.9 \times 1000 \, \text{kg/m}^3$ $\rho_{\text{oil}} = 900 \, \text{kg/m}^3$
Calculate the Reynolds number ( $Re$ ).
The formula for the Reynolds number is:
$Re = \frac{\rho_{\text{oil}} V D}{\mu}$
Substitute the values:
$Re = \frac{(900 \, \text{kg/m}^3) \times (0.60 \, \text{m/s}) \times (0.152 \, \text{m})}{47.9 \times 10^{-3} \, \text{Ns/m}^2}$ $Re = \frac{82.08 \, \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1}}{0.0479 \, \text{Ns/m}^2}$ $Re = \frac{82.08}{0.0479}$ $Re \approx 1713.57$
Determine the type of flow.
For flow in a pipe:
- If $Re < 2000$ , the flow is laminar.
- If $2000 < Re < 4000$ , the flow is transitional.
- If $Re > 4000$ , the flow is turbulent.
Since $Re \approx 1713.57$ , which is less than 2000, the flow is laminar.

The flow is a laminar one.
$\text{Laminar}$

Answer