Fluid Mechanics and Hydraulic Machinery Miscellaneous
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.
- Assuming ideal flow, the force F in newtons required on the plunger to push out the water is
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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 haveP1 + v1² + z1 = P2 + v2² + z2 ρg 2g ρg 2g
Since z1 = z2 and P2 = 0P1 = v2² - v1² ρq 2g 2g P1 = ρ (v2² - v1²) ...(i) 2
Applying continuity equation at points (i) and (ii), we have
A1 v1 = A2 v2⇒ v2 = A1 v1 A2 v2 = [ (π / 4) × (0.01)2 ] v1 [ (π / 4) × (0.001)2 ]
= 100 v1 = 100 × 0.01 = 1 m/s
Now from equation (i),P1 = 1000 [ (1)² - (0.01)² ] = 499.95 N / m² 2
Force required on plunger = P1 × v1= 499.95 × 11 × (0.01)2 = 0.04 N 4
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 haveP1 + v1² + z1 = P2 + v2² + z2 ρg 2g ρg 2g
Since z1 = z2 and P2 = 0P1 = v2² - v1² ρq 2g 2g P1 = ρ (v2² - v1²) ...(i) 2
Applying continuity equation at points (i) and (ii), we have
A1 v1 = A2 v2⇒ v2 = A1 v1 A2 v2 = [ (π / 4) × (0.01)2 ] v1 [ (π / 4) × (0.001)2 ]
= 100 v1 = 100 × 0.01 = 1 m/s
Now from equation (i),P1 = 1000 [ (1)² - (0.01)² ] = 499.95 N / m² 2
Force required on plunger = P1 × v1= 499.95 × 11 × (0.01)2 = 0.04 N 4
- The discharge velocity at the pipe exit in figure is
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By applying Bernoulli’s equation at (1) and (2), we getP1 + V1² + Z1 = P2 + V2² + Z2 ρg 2g ρg 2g
P1 = P2 = Patm
V1 = 0
V2 = ?
Z2 = H – h∴ H = V2² + H - h 2g
V2 = √2gh
Correct Option: B
By applying Bernoulli’s equation at (1) and (2), we getP1 + V1² + Z1 = P2 + V2² + Z2 ρg 2g ρg 2g
P1 = P2 = Patm
V1 = 0
V2 = ?
Z2 = H – h∴ H = V2² + H - h 2g
V2 = √2gh
- For laminar flow through along pipe, the pressure drop per unit length increases
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P1 - P2 = 32μUL D² Correct Option: C
P1 - P2 = 32μUL D²
- In fully developed laminar flow in the circular pipe, the head loss due to friction is directly proportional to _____ (mean velocity/square of the mean velocity)
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f ∝ Mean velocity
Correct Option: A
f ∝ Mean velocity
- Fluid is flowing with an average velocity of V through a pipe of diameter d. Over a length of L,
the head loss is given by fLV² .The friction factor, f for laminar flow in terms of Reynolds 2gD
number (Re) is _______ (fill in the blanks)
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For Laminar flow,
f = 64 Re
Correct Option: B
For Laminar flow,
f = 64 Re