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Drag is defined as forceful pull experienced by the flat plate while the fluid flows over it.
Pressure drag comes from the eddying motions that are set up in the fluid by the passage of the body. This drag is associated with the formation of a wake in the flow.
Frictional drag comes from friction between the fluid and the surfaces over which it is flowing.
For the plate held normal to flow, fluid flows across and there’s huge wake formation occurring behind the plate. As the fluid is not flowing anywhere tangentially to the plate, there is negligible or no viscous drag experienced. So, the total drag on a plate held normal to the flow is equal to pressure drag only.
Figure A: Plate held parallel to the flow ⇒ Only viscous drag takes place
Energy per unit weight of water is used in Bernoulli’s equation to defined energy head at a section.
Bernoulli’s equation is given as
Kinetic energy for the fluid flow is given by
Kinetic energy per unit weight for the fluid flow is given by
Pressure energy for the fluid flow is given by
Continuity Equation is based on the principle of conservation of mass. For a fluid flowing through a pipe at all the cross-section, the quantity of fluid per second is constant.
The continuity equation is given as
Bernoulli’s Equation is based on the principle of conservation of mass. For an ideal fluid flowing through a pipe at all the cross-section, the total energy would be constant.
Displacement thickness,
Momentum thickness,
Energy thickness,
The figure shows curves for velocity distribution across a section for different Reynold’s Number. The curve A corresponds to the Reynold number ___
Laminar flow through a circular pipe follows parabolic velocity distribution.
For the flow through a circular pipe,
Laminar flow – Reynold’s Number is less than 2000
Turbulent Flow – Reynold’s Number is greater than 4000
Transition Flow – Reynold’s Number is between 2000 to 4000
The velocity distribution across a section of two fixed parallel plates is parabolically given by
Where pressure gradient along the length of the plate
y = point of consideration from lower fixed plate
t = distance between the two fixed parallel plates
Pressure head: Head measured due to the pressure experienced/exerted by fluid at the given section.
Kinetic head: Head measured equivalent to the kinetic energy of the fluid in the section.
Potential head: Head attained by the fluid due to its presence at some altitude with reference to the fixed bottom.
Total Head = Pressure Head + Kinetic Head + Potential Head
For the laminar flow through a circular pipe, velocity distribution is parabolic.
Velocity profile is given by,
Maximum velocity is at the center line of the pipe i.e. r = 0
Maximum velocity,
Average velocity,
A controlled mass or closed system is characterized by a fixed quantity of mass of a given identity, while in an open system or control volume mass may change continuously due to the flow of mass across the system boundary.
The continuity equation is the equation of conservation of mass in a fluid flow.
According to the law of conservation of mass:
Rate of flow in section 1 - 1 = Rate of flow at section 2 - 2
This equation is applicable to the compressible as well as incompressible fluid and is called a continuity equation.
If the fluid is incompressible, then ρ1 = ρ2; and continuity equation reduces to A1V1 = A2V2
Type of flow
Reynolds Number
Laminar
Less than 2000
Transition
2000-4000
Turbulent
Greater than 4000
Total acceleration in any direction is given by
Where, is convective acceleration and is local acceleration
u = velocity in the given direction
x = direction of consideration
t = time of consideration
Convective acceleration is defined as the rate of change of velocity due to the change in the position of fluid particles in a fluid flow.
Coefficient of velocity is experimentally determined with the tank with an orifice in the side.
Coefficient of velocity is given by
where, H = Constant head maintained above the center line of the orifice, y = Vertical fall in the level over the distance ‘x’ traveled from the entrance, x = Horizontal distance the fluid has traveled
Note:
Horizontal Distance: x = V × t
Vertical Distance: y
Theoretical velocity:
If a thin plate is held normal to the flow, the viscous drag on it is ______
Viscous force is experienced if the fluid flows along the surface of the plate.
When a plate is held normal to the flow, the water hits the plate perpendicular and wake formation takes place behind the plate which leads to the pressure drag.
Since the flow does not take place along the plate, viscous drag on the plate is zero.
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