Deriving the expression for wind velocity around low pressure area

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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 = Vx i + Vy 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 = rx i + ryj

Eqn for the rotating system is
marot = mainertial - 2m Ω * V - Ω * (Ω * r) ----- (1)

mainertial = -(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. marot = 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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