Presentasi PP Kelompok 2

Ahmad Anggawirya

Indy Prasetya

Jayusandi Mulya Sentosa

Joshua Karubaba

Kezia Dara Euodia

Renno Afriansyah

Stella Faustine Loandy

1406564912

1406604683

1406571470

1406559950

1406567914

1406577783

1406564830

Group 2, no 1. Consider an infinitely long horizontal annulus filled with a Newtonian liquid, the inner tube is moving in x-direction at a constant velocity of v0 and there is no pressure gradient induced from outside (see Figure below). Determine the shell, momentum balance on the shell and find rx and vx respectively as a function of r. Guidance: the flow has the same velocity in x direction, but varied velocity in r direction

Momentum in at surface r

Momentum in at surface r

System is a shear stress driven flow

(2 |(2 ) xr rr

|(2 ) xr r rrL

|(2 ) rx rrL

Total Momentum Balance

Kedua ruas dibagi dengan

| |(2 )( ) 0xr r xr r rrL

(2 )rL r

We know that:

Vx = vx(r) Dan

Vr = 0, v= 0

Boundary Condition (1) :

Boundary Condition (2) :

Group 2, no 2. A liquid (viscosity = 8.9 x 10-4 Pa.s, density = 1000 kg/m3) is flowing at a rate of 0.025 m3/sec/m of width of the plate between two horisontal flat parallel plates. If the distance between the plates is 50mm, calculate: a. maximum velocity, b. the shear stress at the boundaries and c. pressure drop in 1 m of length. Assume laminar flow. Guidance: a. the flow has the same velocity in x (axial) direction, but varied

velocity in y (perpendicular to x) direction b. pressure drop is applied to overcome friction due to shear stress

Information: = . = / = . / = Momentum at surface : In : |= Out : |= Momentum at suface: In : |= Out : |= Momentum at surface

In : | Out : |+

we have information about flux: ( = , = , = = + + = + = + = = + =

so, we have momentum balance: |= |= + |= |= + | |+ = (: )

lim | |+ + |= |= = = + |= |= = = +

= when = , so we get = = to get the velocity we could open the Newtonian principles:

= = = = + we know that = when = =

the velocity distribution is

= = velocity maximum happens at = , = average velocity

mass rate flow

= = = = =

Since the system that we chose only half pipe, then

the mass flow rate for the whole pipe will be

twice

Pressure drop:

a. = = . 28 = , . . . , . = ,.

b. = = = , . B.C.

X=0; =0 X==. = , . . = ,.

THANK YOU !