FLUIDS PROBLEM 14–11
ELEMENT VELOCITY COMPONENTS
ELEMENT VEL(X) VEL(Y)
11 – 0.12222E+05 – 0.19572E+04
12 – 0.49369E+04 – 0.92425E+04
13 – 0.14055E+05 – 0.14229E+05
14 0.74983E+04 – 0.14229E+05
15 0.81240E+04 – 0.12092E+05
26 – 0.56043E+04 – 0.21350E+04
27 – 0.67102E+04 – 0.20719E+04
28 – 0.27549E+04 – 0.60273E+04
29 – 0.41023E+04 – 0.72286E+04
30 0.31961E+04 – 0.72286E+04
41 – 0.40618E+04 0.16983E+04
42 – 0.40618E+04 – 0.16833E+04
43 – 0.45923E+04 – 0.17156E+04
44 – 0.18482E+04 – 0.44597E+04
45 – 0.23311E+04 – 0.50048E+04
551
55 – 0.18156E+04 0.38847E+04
56 – 0.40301E+04 0.16702E+04
RESULTANT NODAL VALUES
1 – 0.49446E+03
2 0.23005E+02
13 0.23855E+03
14 0.84934E+02
15 0.14912E+03
16 0.22760E+03
17 0.25296E+03
28 0.50000E+03
29 0.50000E+03
30 0.50000E+03
31 0.50000E+03
32 0.50000E+03
14.12
LOADING CASE 1
0 0.00000E+00
*PRESCRIBED NODAL VALUES*
NODAL VALUES, LOADING CASE 1
552
14.13 Use
1
4
of the whole system due to symmetry
LOADING CASE 1
0 0.00000E+00
LOADING CASE 2
25 0.12500E+03 (pumping rate)
*PRESCRIBED NODAL VALUES*
NODAL VALUES, LOADING CASE 1
1 0.10000E+03 2 0.10000E+03
5 0.10000E+03 6 0.10000E+03
9 0.10000E+03 10 0.10000E+03
NODAL VALUES, LOADING CASE 2
1 0.10000E+03 2 0.10062E+03
5 0.10202E+03 6 0.10000E+03
9 0.10177E+03 10 0.10209E+03
13 0.10125E+03 14 0.10185E+03
RESULTANT NODAL VALUES
1 0.10000E+03
553
2 0.10062E+03
3 0.10121E+03
4 0.10174E+03
15 0.10231E+03
16 0.10000E+03
17 0.10063E+03
18 0.10128E+03
ELEMENT VELOCITY COMPONENTS
ELEMENT VEL (X) VEL (Y)
2 0.79155E–04 0.21935E–04
4 0.17643E–04 0.41962E–04
5 0.11921E–03 0.00000E+00
7 0.12875E–04 0.21935E–04
9 0.12207E–03 0.57220E–05
11 0.14305E–04 0.47684E–05
14 0.92506E–04 0.57220E–05
16 0.45300E–04 0.47684E–05
18 0.94414E–04 0.28610E–04
20 0.48161E–04 0.95367E–06
21 0.11921E–03 0.00000E+00
23 0.95367E–05 0.28610E–04
25 0.12207E–03 0.57220E–05
27 0.17643E–04 – 0.19073E–04
30 0.80585E–04 0.57220E–05
32 0.45300E–04 – 0.19073E–04
14.17
I1 0 I1 I2
[k(1)] =
80 80
80 80
, [k(2)] =
55
55
[k(7)] =
55
55
, [k(8)] =
55
55
I1 I2 I3
1
2
3
I
I
125 5 0
0 10 20
11
22
33
II
II
20
10
IAD = I1 – I2
IBC = I2 – I3
Using Mathcad
125 – 5 0
0 – 10 20
20
–10
0.161
14.18
Resistor element stiffness matrices.
I1 0 I1 I3
[k(1)] =
11
10 11
, [k(2)] =
11
511
2
1
AMPS
– 5 – 20 85
0
AMPS1 = 1solve (K1, V1) AMPS1 =
– 0.853
– 0.458
– 0.158
1
AB
I
=
0
1
AMPS
–
2
1
AMPS
1
AB
I
= – 0.695
I1 I2 I2 0
221 221
221 221
383 383
383 383
221 221
221 221 383
1
2
I
I
=
12
0
IAD = I1 – I2 if < 0.015 amp R1 acceptable
If I2 < 0.015 amp R2 acceptable
IBD = I1
ICD = I2
[k20] =
221 – 221
– 221 221 383
{v20} =
12
0
0
2
0
2
0.086
0.031
Must increase ohms size so amps < 0.015. Try previous final R’s of 715 and 806 ohms from
0
2
0
2
0.015
Still amps too large in diodes under R1 (Try 2000 ohm for R1 and 1270 ohms for R2)
2000 – 2000
14.23