Lecture 4Lecture 4

Pressure variation in a static Pressure variation in a static fluidfluid

N.S. Equations & simple N.S. Equations & simple solutionssolutions

Intro DLIntro DL

Pressure variation in a static Pressure variation in a static fluidfluid

Consider a differential element in a viscous fluid

fyxa x

xyxxx

Navier Stokes Equations

N-S-E in index notation

Xu

Xg

XP

tDuD

j

i

j

i

i

i

2

Xu

utu

tDuD

j

ij

ii

Navier Stokes EquationsIn 3-d

Navier Stokes EquationsNavier Stokes Equations

• Governing Governing equations for flow equations for flow of viscous fluids of viscous fluids (equations of (equations of motion)motion)

Flow through Simple Flow through Simple geometriesgeometries• Capillary tubeCapillary tube

• Between parallel Between parallel platesplates

Darcy’s observation & Law

Darcy’s observation & Law

• One form of Darcy law

hKq^^

hI ^^

Constant head permeameter

Falling head permeameter