Chapter 3, Problem 3.4P

(a)

Interpretation Introduction

Interpretation:

The transition length at the pipe entrance for the flow of glycerol is to be calculated.

Concept Introduction:

The formula to calculate the transition length $\left(x_t\right)$ for a laminar flow $\left(N_{\mathrm{Re}}<2100\right)$ is:

  $\frac{x_t}{D}=0.05N_{\mathrm{Re}}$ ...... (1)

Here, $D$ is the pipe diameter and $N_{\mathrm{Re}}$ is the Reynolds number defined as:

  $N_{\mathrm{Re}}=\frac{D\overline{V}\rho }{\mu }$ ...... (2)

Here, $\overline{V}$ is the average liquid velocity, $\rho$ is the density of the fluid, $\mu$ is the viscosity of the fluid, and $D$ is the pipe diameter.

For turbulent flow $\left(N_{\mathrm{Re}}>4000\right)$ , the transition length at the pipe entrance is independent of the Reynolds number and is only dependent on the pipe diameter, that is, about 40 to 50 times the diameter of the pipe having very small differences in distribution at about 25 diameters.

(b)

Interpretation Introduction

Interpretation:

The transition length at the pipe entrance for the flow of n -propyl alcohol is to be calculated.

Concept Introduction:

The formula to calculate the transition length $\left(x_t\right)$ for a laminar flow $\left(N_{\mathrm{Re}}<2100\right)$ is:

  $\frac{x_t}{D}=0.05N_{\mathrm{Re}}$ ...... (1)

Here, $D$ is the pipe diameter and $N_{\mathrm{Re}}$ is the Reynolds number defined as:

  $N_{\mathrm{Re}}=\frac{D\overline{V}\rho }{\mu }$ ...... (2)

Here, $\overline{V}$ is the average liquid velocity, $\rho$ is the density of the fluid, $\mu$ is the viscosity of the fluid, and $D$ is the pipe diameter.

For turbulent flow $\left(N_{\mathrm{Re}}>4000\right)$ , the transition length at the pipe entrance is independent of the Reynolds number and is only dependent on the pipe diameter, that is, about 40 to 50 times the diameter of the pipe having very small differences in distribution at about 25 diameters.