Introduction to Food Engineering Unit 2 Fluid Flow in Food Processing

Liquid Transport Systems Pipelines for Processing Plants

Types of Pumps

2. Properties of Liquids 1. Role of Stress in Fluid Flow Stress = force / unit area, normal stress = pressure Shear stress --> flow

Fig. 2.7 Illustration of drag generated on underlying cards as the top card in a deck is moved. This is analogous to the movement of the top layer of a fluid.

Density Mass per unit volume, kg/m3 Depend on temperature Measured by hydrometer compared with water

Resistance to shear force Viscosity Resistance to shear force (2.1) (2.2) (2.3)

Viscosity du/dy = shear rate  = coefficient of viscosity Newtonian liquid unit  = N/m2 = Pa  = Pa.s

Example Determine shear stress for water at ambient temperature when exposed to a shear rate of 100 s-1 Given viscosity of water at ambient temp = 10-3 Pa.s  =  du/dy = (10-3 Pa.s)(100 s-1) = 0.1 Pa

Measurement of Viscosity Capillary Tube Viscometer

(2.4) (2.5) (2.6)

(2.7)  = 0 at center of tube, r = R at wall (2.8) (2.9)

(2.10) (2.11) (2.12) Cross sectional area of a shell in tube

Vol flow rate = u . dA . (2.13) . (2.14) . (2.15)

(2.16) . See example Tube length L, radius R Measure Vol flow rate at pressure P See example

Example Measure viscosity of honey at 30 C. Tube radium 2.5 cm, length 25 cm. P (Pa) V (cm3/s)  (Pa.s) 10 1.25 4.909 12.5 1.55 4.948 15.0 1.80 5.113 17.5 2.05 5.238 20.0 2.55 4.812

(2.17) (2.18) If allow gravitational force to provide P for flow (P = F/A, F = ma)

(2.19) Since V = R2L, m = V (2.20) Measure time of liquid mass, m flow in tube length, L

Rotational Viscometer

Rotational Viscometer torque (2.21) Shear rate,   Angular velocity,  (2.22)

 = Integrate between outer & inner cylinders (2.24) (2.25)

(2.26) N = revolution per sec (2.27)  Measurement of  at given N

(2.28) Outer radius Ro ->  Single-cylinder viscometer Assuming container wall has no influence on shear stress (2.28)

Single-cylinder viscometer 1 cm radius 6 cm length N (rpm)  (x 10-3 N.cm)  (Pa.s) 3 1.2 0.507 6 2.3 0.485 9 3.7 0.521 12 5.0 0.528

N = 3 rpm = 3/60 rev/sec = 0.05 rev/s L = 0.06 m Ri = 0.01 m = 1.2 x 10-3 N.cm = 1.2 x 10-5 N.m  = 0.507 Pa.s

Influence of Temperature on Viscosity (2.29) BA = Arrhenium constant Ea = activation energy constant Rg = gas constant