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0

$begingroup$

I'm trying to get a linearized model for a physical system, but I've got an asymptote in the linearized equation that I don't know how to deal with.
I have Bernoulli's equation

$P_o = P + 1/2rho v^2$

solved for velocity.

$v = sqrtfrac2(P_o-P)rho$

I would like a linearized equation so that I can use it as a linear model.

I've taken the derivative with respect to $Delta P$

$Delta P = P_o - P$

so that

$fracdvdt = frac1sqrt2rho Delta Pdelta Delta P$

My questions are:

1) Is this the proper approach to linearizing this equation?

2) How do I deal with an asymptote, in what should be the physical realm with no disconnect?

asymptotics linearization

share|cite|improve this question

asked Mar 12 at 20:58

BotoBoto

113

$endgroup$

add a comment | 

0

$begingroup$

I'm trying to get a linearized model for a physical system, but I've got an asymptote in the linearized equation that I don't know how to deal with.
I have Bernoulli's equation

$P_o = P + 1/2rho v^2$

solved for velocity.

$v = sqrtfrac2(P_o-P)rho$

I would like a linearized equation so that I can use it as a linear model.

I've taken the derivative with respect to $Delta P$

$Delta P = P_o - P$

so that

$fracdvdt = frac1sqrt2rho Delta Pdelta Delta P$

My questions are:

1) Is this the proper approach to linearizing this equation?

2) How do I deal with an asymptote, in what should be the physical realm with no disconnect?

asymptotics linearization

share|cite|improve this question

asked Mar 12 at 20:58

BotoBoto

113

$endgroup$

add a comment | 

$begingroup$

I'm trying to get a linearized model for a physical system, but I've got an asymptote in the linearized equation that I don't know how to deal with.
I have Bernoulli's equation

$P_o = P + 1/2rho v^2$

solved for velocity.

$v = sqrtfrac2(P_o-P)rho$

I would like a linearized equation so that I can use it as a linear model.

I've taken the derivative with respect to $Delta P$

$Delta P = P_o - P$

so that

$fracdvdt = frac1sqrt2rho Delta Pdelta Delta P$

My questions are:

1) Is this the proper approach to linearizing this equation?

2) How do I deal with an asymptote, in what should be the physical realm with no disconnect?

asymptotics linearization

share|cite|improve this question

asked Mar 12 at 20:58

BotoBoto

113

$endgroup$

share|cite|improve this question

asked Mar 12 at 20:58

BotoBoto

113

share|cite|improve this question

asked Mar 12 at 20:58

BotoBoto

113

asked Mar 12 at 20:58

BotoBoto

113

asked Mar 12 at 20:58

BotoBoto

113