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Hi
Can somebody tell me the steps and assumptions made in deriving the equation to calculate the wind velocity around a low pressure area ? (see the attachment fro Kleppner & Kolenkow).
I tried to derive like this :
Coordinate system located on earth's surface with i direction towards E, j direction towards N and k direction upwards.
Initial wind velocity V = V_{x} i + V_{y} j
Ω = Ω sin λ j + Ω cos λ k where λ is the latitude of the place considered.
Position vector of parcel of air r = r_{x} i + r_{y}j
Eqn for the rotating system is
ma_{rot} = ma_{inertial}  2m Ω * V  Ω * (Ω * r)  (1)
ma_{inertial} = (ΔP)S j where S = cross sectional area of parcel of air
As the flow is assumed to be steady, LHS of equation 1 i.e. ma_{rot} = 0
RHS evaluated vectorially.
However, I cannot get the expression shown in the attachment.
Please help out. Is there any other text which shows this derivation ?
TIA
Can somebody tell me the steps and assumptions made in deriving the equation to calculate the wind velocity around a low pressure area ? (see the attachment fro Kleppner & Kolenkow).
I tried to derive like this :
Coordinate system located on earth's surface with i direction towards E, j direction towards N and k direction upwards.
Initial wind velocity V = V_{x} i + V_{y} j
Ω = Ω sin λ j + Ω cos λ k where λ is the latitude of the place considered.
Position vector of parcel of air r = r_{x} i + r_{y}j
Eqn for the rotating system is
ma_{rot} = ma_{inertial}  2m Ω * V  Ω * (Ω * r)  (1)
ma_{inertial} = (ΔP)S j where S = cross sectional area of parcel of air
As the flow is assumed to be steady, LHS of equation 1 i.e. ma_{rot} = 0
RHS evaluated vectorially.
However, I cannot get the expression shown in the attachment.
Please help out. Is there any other text which shows this derivation ?
TIA
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