2. • Introduction
• Whenever a solid body is held in the path of moving fluid and
it is completely immersed in it, it experiences some force or
pressure.
• Conversely, if the body is moving with uniform velocity
through a still fluid, it experiences some resistance and has to
work against that resistance for steady movement.
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Flow around immersed bodies
3. • If a plate is immersed in a liquid parallel to the flow, it will
experience pressure less than that pressure experienced by the
body if it is immersed perpendicular to the flow.
• When a plate is held at an angle with the direction of flow of
liquid, the streamlines of the liquid get deflected.
• The pressure exerted by the fluid is the same, when fluid is at
rest and object is moving uniformly through it and vice versa.
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4. • Newton’s Law of Resistance
• “The force exerted by a moving fluid on an immersed body is
directly proportional to the rate of change of momentum due to
the presence of the body”
• Mathematically,
P 𝛂
𝛚𝐚𝐕𝟐
𝐠
= k .
𝛚𝐚𝐕𝟐
𝐠
Where,
k = constant of proportionality
ω = Specific weight of fluid
a = area of body
V = velocity of fluid
g = gravitational constant
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5. Assumptions for Newton’s Law:
1. Planes of the body are completely smooth.
2. Space around the body is completely filled with fluid.
3. Fluid has a large number of fine particles having mass
but no dimensions.
4. Fluid particle do not exert any influence on one another.
5. Body experiences impact from all the particles in its
path.
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Discrepancy in Newton’s Law:
1. It takes into account only the conditions at the front of
the body while those at the sides and tail are ignored.
2. The motion of fluid particles is always influenced by its
neighboring particles.
6. • Newton’s assumptions found that:
k = 1
• But later experimentally it was calculated as:
k = 0.55
So,
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P = 0.5 .
𝛚𝐚𝐕𝟐
𝐠
7. • The pressure exerted by the fluid will be at right angle to the
plate and it has two components; Lift and Drag.
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𝑷𝑫 = 0.5 .
𝛚𝐚𝐕𝟐
𝐠
. 𝒔𝒊𝒏 𝜶 = 𝑲𝑫 .
𝛚𝐚𝐕𝟐
𝟐𝐠
1- Drag Force (Horizontal)
2- Lift Force (Vertical)
𝑷𝑳 = 0.5 .
𝛚𝐚𝐕𝟐
𝐠
. 𝒄𝒐𝒔 𝜶 = 𝑲𝑳 .
𝛚𝐚𝐕𝟐
𝟐𝐠
3- Resultant Force
𝑹 = 𝑷𝑫
𝟐
+ 𝑷𝑳
𝟐
8. Examples
• A flat plate 2m *2 m is immersed in water flowing with a
velocity of 5 m/s. find the forces of drag and lift . Take Kd=0.05
and kl=0.2
• A circular disc 3 m diameter is held normal to a 15 m/s wind
having specific weight of 11.8 N/m3. if the drag coefficient is
0.4, find the force required to hold it.
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