Draw schemes of viscose air flow about solid body surface. Mark main elements of this flow.
Relation between which forces does Reynolds number (Re) characterize? Write the formula for Reynolds number calculation, call physical values used in this formula.
The Reynolds number is a ratio of forces due to inertia and viscosity.
Therefor, the Reynolds number is given by
l – is a characteristic length
A=l2
Therefore,
The value of the Reynolds number in a flow gives an idea about its nature. For example, at higher Reynolds numbers the magnitude of viscous forces is small compared to the enertia forces.
Relation between which forces does Fruds number (Fr) characterize? Write the formula for Fruds number calculation, call physical values used in this formula.
The Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of a partially submerged object moving through water, and permits the comparison of objects of different sizes.
The Froude Number is a dimensionless parameter measuring of the ratio of the inertia force on a element of fluid to the weight of the fluid element - the inertial force divided by gravitational force.
The Froude Number can be expressed as
Fr = v / (g l)1/2
Where: Fr = Froude number, v = velocity, g = gravity
l = characteristic length
The Froude Number is relevant in fluid dynamic problems where the weight of the fluid is an important force.
In general this is the situation for free surfaces like cold windows and hot radiators. It is used in momentum transfer in general and open channel flow and wave and surface behavior calculations in particular.
The Froude Number is also important in analyzing flow in spillways, weirs, channel flows, rivers and ship design.
The Froude number is a ratio of inertial and gravitational forces.
Gravity (numerator) - moves water downhill
Inertia (denominator) - reflects its willingness to do so.
Where:
V = Water velocity
D = Hydraulic depth (cross sectional area of flow / top width)
g = Gravity
When:
Fr = 1, critical flow,
Fr > 1, supercritical flow (fast rapid flow),
Fr < 1, subcritical flow (slow / tranquil flow)
The Froude number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.
Relation between which forces does Eulers (Eu) number characterize? Write the formula for Eulers number calculation, call physical values used in this formula.
The Euler Number is a dimensionless value commonly used for analyzing fluid flow dynamics problems where the pressure difference between two points is important. The Euler number Eu characterizes the relation between the pressure forces acting on an elementary volume of a liquid or gas and the inertia forces The Euler Number can be expressed as
Eu = p / (ρ v2)
where
Eu = Euler number
p = pressure (Pa)
ρ = density (kg/m3)
v = fluid flow velocity (m/s)
The pressure difference as indicated below is often used
Eu = dp / (ρ v2)
where
dp = differential pressure (Pa)
Note! - a perfect frictionless flow corresponds to an Euler number of 1
The combination below is called the pressure coefficient
pressure coefficient = dp / (1/2 ρ v2) (3)
where
is
the density of the fluid.
is
the upstream pressure.
is
the downstream pressure.
is
a characteristic velocity of the flow.