stroupaloop
Mechanical
I have been thumbing through the forum posts lately and figure that now is a as good of time as any to begin discussing different modeling equations necessary to calculate various fluid conditions of a system. I suppose coming from a mathematical background and my shear lack of faith in much of anything without analytical calculations justified why I enjoy mathematical modeling of the system. All calculations done will be at a steady state condition due to the introduction to non-linear differential equations required for dynamic analysis.
These forums are open to discussion and I look forward to people's feedback. I will attempt to post a new modeling equation when I have time.
Flow Restrictor Model Equation:
As we should all know as engineers, there are three types of flow conditions: laminar, transitional, and turbulent. Since the transitional phase is so unpredictable, we will only focus on laminar and turbulent conditions for now.
General Flow Restrictor Model Equation:
Q = K(r)*A(r)*deltaP^n
where:
Q = flow
K(r) = flow coefficient
A(r) = flow area
deltaP = pressure differential
n = exponent (0.5 for turbulent and 1 for laminar)
As everyone can see, to complete the equation, the remaining variable becomes K(r) which varies depending on the state of fluid being either laminar or turbulent.
Turblent:
K(r) = C(d)*(2/rho)^0.5
where:
C(d) = flow coefficient (assumed to be 0.61 from experimental data)
rho = fluid density
Laminar:
K(r) = D(r)^2/(32*mu*L)
where:
D(r) = flow diameter
mu = dynamic viscosity
L = restriction length
It is important to note that this equation is a general model for flow restrictors. An assumption that a sharp edged orifice is used. As the orifice changes, so does the design parameters on the equation. Additionally, flow will never be specifically laminar or turblent which means your "n" value will typically be in between 0.5 and 1. Both "actual" changes in phsyical representation of the equation requires experimental data to verify such results, but this equation is best suited for modeling general steady state parameters.
These forums are open to discussion and I look forward to people's feedback. I will attempt to post a new modeling equation when I have time.
Flow Restrictor Model Equation:
As we should all know as engineers, there are three types of flow conditions: laminar, transitional, and turbulent. Since the transitional phase is so unpredictable, we will only focus on laminar and turbulent conditions for now.
General Flow Restrictor Model Equation:
Q = K(r)*A(r)*deltaP^n
where:
Q = flow
K(r) = flow coefficient
A(r) = flow area
deltaP = pressure differential
n = exponent (0.5 for turbulent and 1 for laminar)
As everyone can see, to complete the equation, the remaining variable becomes K(r) which varies depending on the state of fluid being either laminar or turbulent.
Turblent:
K(r) = C(d)*(2/rho)^0.5
where:
C(d) = flow coefficient (assumed to be 0.61 from experimental data)
rho = fluid density
Laminar:
K(r) = D(r)^2/(32*mu*L)
where:
D(r) = flow diameter
mu = dynamic viscosity
L = restriction length
It is important to note that this equation is a general model for flow restrictors. An assumption that a sharp edged orifice is used. As the orifice changes, so does the design parameters on the equation. Additionally, flow will never be specifically laminar or turblent which means your "n" value will typically be in between 0.5 and 1. Both "actual" changes in phsyical representation of the equation requires experimental data to verify such results, but this equation is best suited for modeling general steady state parameters.
