Direction: A syringe with a frictionless plunger contains water and has at its end a 100 mm long needle of 1 mm diameter. The internal diameter of the syringe is 10 mm. Water density is 1000 kg/m3. The plunger is pushed in at 10 mm/s and the water comes out as a jet. 
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Assuming ideal flow, the force F in newtons required on the plunger to push out the water is
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- 0
- 0.04
- 0.13
- 1.15
- 0
Correct Option: B
ρwater =1000 kg/m3
Velocity at points 1 = velocity of plunger = 10 mm/ s = 0.014 m/s 
Applying Bernoulli’s equation at points 1 and 2, we have
| + | + z1 = | + | + z2 | |||||
| ρg | 2g | ρg | 2g |
Since z1 = z2 and P2 = 0
| = | - | ||||
| ρq | 2g | 2g |
| P1 = | (v2² - v1²) ...(i) | |
| 2 |
Applying continuity equation at points (i) and (ii), we have
A1 v1 = A2 v2
| ⇒ v2 = |  |  | v1 | |
| A2 |
| v2 = | v1 | |
| [ (π / 4) × (0.001)2 ] |
= 100 v1 = 100 × 0.01 = 1 m/s
Now from equation (i),
| P1 = | [ (1)² - (0.01)² ] = 499.95 N / m² | |
| 2 |
Force required on plunger = P1 × v1
| = 499.95 × | × (0.01)2 = 0.04 N | |
| 4 |
