If there was a small sphere freely suspended in plane poiseuille flow, how would you go about using linearity to prove that the
1 answer:
Answer Explanation :
Poiseuille equation: this equation is used for non ideal flow this is used for the calculation of pressure in laminar flow it is physical law we know that fluid in laminar flow, flows across the pipe whose diameter is larger than the length of pipe
in mathematical form the equation can be expressed as
Q =
where η is the cofficient of viscosity
now if we assume a small sphere of radius a is suspended freely in the plane of the laminar flow then for assuring that the sphere does not migrate with the flow we have to calculate the rate of flow of the liquid
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To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.
Here,
M = Mass
R = Radius of the hoop
The precession frequency is given as
Here,
M = Mass
g= Acceleration due to gravity
d = Distance of center of mass from pivot
I = Moment of inertia
= Angular velocity
Replacing the value for moment of inertia
The value for our angular velocity is not in SI, then
Replacing our values we have that
The precession frequency is
Therefore the precession period is 5.4s