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14. Pressure Velocity Trade off :
For a fluid flowing at a horizontal level according to (Bernoulli's Theorem) we use.
P + ½ ρ v2 = constant [No difference in potential energies on same
horizontal level].
If velocity Pressure
If velocity Pressure
This pressure difference causes
the aeroplane to fly providing the lifting force
VA < VB
PA > PB
15. Pressure Velocity Trade off :
For a fluid flowing at a horizontal level according to (Bernoulli's Theorem) we use.
P + ½ ρ v2 = constant [No difference in potential energies on same
horizontal level].
If velocity Pressure
If velocity Pressure
This pressure difference causes
the aeroplane to fly providing the lifting force
VA < VB
PA > PB
23. Px < Py
Vx > Vy
Liquid sprays application
X
Y
Example 2. Atomizer Spray
24. The ball keeps floating as moves left & right in stable equilibrium.
Air blow
Air blow Air blow
Example 3.
25. Air blow
High velocity
Low Pressure
Air blow
Low velocity
High Pressure
Air blow
High velocity
Low Pressure
Low velocity
High Pressure
The ball keeps floating as moves left & right in stable equilibrium.
Example 3.
26. In a horizontal pipe line, the following oil pressure falls by 8 N/m2 between 2 points
separated by 1 km. Find the change in kinetic energy per kg of oil at these points.
Take density of oil 800 kg/m3
A. 0.01 J/kg
B. 0.02 J/kg
C. 0.03 J/kg
D. 0.04 J/kg
1000 m
P1
P2 = (P1-8)
ρ = 800 kg/m3
28. Calculate the gross lift force on an airplane wing of length 10 m and width 2 m. The
air speed above the wing is 120 m/s and below the wing is
90 m/s. Take air density 1.3 kg/m3.
A. 6.2 x 104 N
B. 8.2 x 104 N
C. 10.2 x 104 N
D. 12.2 x 104 N
30. Water flows through a tube which has one end A with cross-sectional area 1 cm2 and other
end B with cross-sectional area 0.5 cm2. The speed of water at A is 10 cm/s find the speed
at B & pressure difference at A & B.
A. 20 cm/s, 225 N/m2
B. 20 cm/s, 485 N/m2
C. 15 cm/s, 635 N/m2
D. 15 cm/s, 875 N/m2
A
B
20 cm
15 cm
1 cm2
0.5 cm2
10 cm/s
36. In a bucket shown in figure a liquid of density 103 kg/m3 is kept. Find speed at
which liquid will be coming out if the bottom surface is removed and its top level is
maintained by pouring the liquid through the tap.
A. 4 m/s
B. 3 m/s
C. 2 m/s
D. 1 m/s
vA
A
B
vB
0.75m
10 cm
5 cm
40. Working & Application of a ‘PITOT TUBE’
h
A B
Pitot Tube
A device used to measure flow velocity of a fluid
First calculate the velocity of air relative to the plane indirectly that would be the speed in opposite
direction
Can be used to calculate the velocity of aeroplanes
ρ
ρg
vg
41. Working & Application of a ‘PITOT TUBE’
h
A B
Pitot Tube
A device used to measure flow velocity of a fluid
PA - PB = hρg PA - PB = h ( ρ - ρL ) g
Gaseous medium flowing If flowing fluid is a liquid
Bernoulli’s Theorem (A) - (B) for flowing fluid.
PA + 0 = PB + ½ ρg vg
2
v =
√ 2(PA - PB)
ρg
First calculate the velocity of air relative to the plane indirectly that would be the speed in opposite direction
Can be used to calculate the velocity of aeroplanes
ρ
vg
44. Working & Application of ‘VENTURIMETER’
A device used to measure flow velocity of liquid in pipelines
pipe
2 1
v2
h
Pressure
Tubes
Patm
area = A
area =a
v1
v1 = ?
v1
ρ
Patm
area = A
45. Working and Application of ‘VENTURIMETER’
A device used to measure flow velocity of liquid in pipelines
pipe
v1
A B
v2
h
Pressure
Tubes
Patm
Patm+ hρg
Continuity Equation :
A1v1 = A2v2 v2 = [A1/A2]v1
A1
A1 A2
v1
v1 = ?
Using Bernoulli’s Theorem (A) - (B)
½ ρv2
2 + PA = ½ ρ v1
2 + PB
½ ρ (v2
2 - v1
2 ) = PB - PA
½ ρ (v2
2 - v1
2 ) = hρg
½ v1
2 [A1
2 / A2
2 -1 ] = hg
v1 = √ 2gh
[A1
2 / A2
2 - 1]
PA = Patm + xρg
PB = Patm + hρg+xρg
PB - PA = hρg
46. In a venturimeter diameter of the pipe is 4 cm and that of constriction is
3 cm. When flows the heights of water level in pressure tubes are 15 cm and
20 cm. Find the discharge rate of pipe. (Take g = 10 m2)
v
1
v2
5 cm
d=3 cm
D=4 cm
ρ
48. Water flows through the tube shown in figure. The areas of cross-section of wide
and narrow sections are 5 cm2 and 2 cm2 respectively. Rate of water flow in tube is
500 cm3/sec. Find the difference in mercury levels in the U-tube.
A. 1.98 cm
B. 2.08 cm
C. 2.69 cm
D. 3.02 cm
A B
5 cm2
2 cm2 ρ
13.6 ρ
h
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