Download - Presentasi Pp Klpk 2
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Presentasi PP Kelompok 2
Ahmad Anggawirya
Indy Prasetya
Jayusandi Mulya Sentosa
Joshua Karubaba
Kezia Dara Euodia
Renno Afriansyah
Stella Faustine Loandy
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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
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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
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Total Momentum Balance
Kedua ruas dibagi dengan
| |(2 )( ) 0xr r xr r rrL
(2 )rL r
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We know that:
Vx = vx(r) Dan
Vr = 0, v= 0
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Boundary Condition (1) :
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Boundary Condition (2) :
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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
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Information: = . = / = . / = Momentum at surface : In : |= Out : |= Momentum at suface: In : |= Out : |= Momentum at surface
In : | Out : |+
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we have information about flux: ( = , = , = = + + = + = + = = + =
so, we have momentum balance: |= |= + |= |= + | |+ = (: )
lim | |+ + |= |= = = + |= |= = = +
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= when = , so we get = = to get the velocity we could open the Newtonian principles:
= = = = + we know that = when = =
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the velocity distribution is
= = velocity maximum happens at = , = average velocity
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mass rate flow
= = = = =
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Since the system that we chose only half pipe, then
the mass flow rate for the whole pipe will be
twice
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Pressure drop:
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a. = = . 28 = , . . . , . = ,.
b. = = = , . B.C.
X=0; =0 X==. = , . . = ,.
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THANK YOU !