Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Orange JO A
O X 91|4 2:26
ch1_introductio..
Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A
Water responds to shear stress by continuously yielding in angular deformation in the
direction of the shear.
IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear
Istress, as shown in Figure 1.1.
do
dt
dx
,and v =
dy
dx
Angular deformation (Shear strain), 0 =
dt
do
Rate of shear strain =
dt
dx
dv
(Velocity gradient)
dy
dy dt
dv
Therefore, to
dv
T = constant
dy
dv
T = -
dy
The proportionally constant, u, is called the absolute viscosity of the flyid
Example
A flat plate of 50 cm² is being pulled over a fixed
flat surface at a constant velocity of 45 cm/sec
(Figure 1.1). An oil film of unknown viscosity
separates the plate and the fixed surface by a
distance of 0.1 cm. The force (T) required to pull
the plate is measured to be 31.7 N, and the viscosity
E of the fluid is constant. Determine the viscosity
(absolute).
22
Example
A flat plate of 50 cm² is being pulled over a fíxed flå
!constant velocity of 45 cm/sec (Figure 1.1). An oil fih.
unknown viscosity separates the plate and the fixed surface by a
at a
Transcribed Image Text:Orange JO A O X 91|4 2:26 ch1_introductio.. Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A Water responds to shear stress by continuously yielding in angular deformation in the direction of the shear. IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear Istress, as shown in Figure 1.1. do dt dx ,and v = dy dx Angular deformation (Shear strain), 0 = dt do Rate of shear strain = dt dx dv (Velocity gradient) dy dy dt dv Therefore, to dv T = constant dy dv T = - dy The proportionally constant, u, is called the absolute viscosity of the flyid Example A flat plate of 50 cm² is being pulled over a fixed flat surface at a constant velocity of 45 cm/sec (Figure 1.1). An oil film of unknown viscosity separates the plate and the fixed surface by a distance of 0.1 cm. The force (T) required to pull the plate is measured to be 31.7 N, and the viscosity E of the fluid is constant. Determine the viscosity (absolute). 22 Example A flat plate of 50 cm² is being pulled over a fíxed flå !constant velocity of 45 cm/sec (Figure 1.1). An oil fih. unknown viscosity separates the plate and the fixed surface by a at a
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