Answered: Pure milk at 293 K has a density of…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Question

Pure milk at 293 K has a density of 1030 kg / m3 and a viscosity of 2.12 cp flowing at a rate of 1,405 kg / s in a pipe having a diameter of 70 mm.
a. Calculate the Reynolds number. =
b. Is the flow turbulent
No or Yes
.
c. The flow velocity required for Reynold's number 2100 is = m / s.

Expert Solution

Step 1

Given:

$ρ = 1030 \frac{kg}{m^{3}} μ = 2.12 cP = 2.12 \times 10^{- 3} Pa·s \dot{m} = 1405 \frac{kg}{s} D = 70 mm = 0.07 m$

Step 2

Area can be calculated from its formula,

$\begin{array}{rcl} A & = & \frac{π D^{2}}{4} \\ = & \frac{3.14 \times {(0.07 m)}^{2}}{4} \\ = & 0.00385 m^{2} \end{array}$

We can calculate volumetric flow rate, Q as follows:

$\begin{array}{rcl} Q & = & \frac{Mass flow rate, \dot{m}}{Density, ρ} \\ = & \frac{1405 \frac{kg}{s}}{1030 \frac{kg}{m^{3}}} \\ = & 1.364 \frac{m^{3}}{s} \end{array}$

From the formula of volumetric flow rate, we can calculate the velocity such as,

$\begin{array}{rcl} v & = & \frac{Q}{A} \\ = & \frac{1.364 \frac{m^{3}}{s}}{0.00385 m^{2}} \\ = & 354.28 \frac{m}{s} \end{array}$

Thus, the velocity is $\begin{array}{rcl} 354 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 28 \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} \frac{m}{s} \end{array}$ .

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