Direction: Consider a linear programming problem with two variable and two constraints. The objective function is maximize x1 + x2. The corner points of the feasible region are (0, 0), (0,2) (2, 0) and (4/3, 4/3)
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Oil is being pumped through a straight pipe, the pipe length, diameter and volumetric flow rate are all doubled in a new arrangement. The pipe friction factor, however, remains constant. The ratio of pipe frictional losses in the new arrangement to that in the original configuration would be
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- 1/4
- 1/2
- 2
- 4
Correct Option: A
For original configuration
l1 = l
d1 = d
Q1 = Q
For new configuration
l2 = 21
d2 = 2d
Q2 = 2Q
Head loss due to friction,
| hf = | |
| 2gb |
where f = friction factor
l = Length of pipe
v = Average velocity
d = Diameter pipe
| Discharge: Q = AV = | a²V | |
| 4 |
| or V = | |
| πa² |
| hf = | × |  |  | ² | = | |||
| 2gd | πa² | πga5 |
For new Pipe,
| hf2 = | = | = | |||
| πgda5 | π × 25 × a5 | πga5 |
| = | × | = | ||||
| h2² | πga5 | 2flQ² | 4 |
