The similarity relations for Prandtl-Meyer expansion wave may also be written in terms of the similarity parameter. The flow through an expansion fan is isentropic. Hence, the isentropic relations for pressure can be used for the conditions on both sides of expansion fan. When approximated to hypersonic flows, the static pressure relation across the expansion fan can be written as below;

(4.7.20)

Rearranging Eq. (4.7.15), the ratio of Mach numbers across the expansion wave can be obtained.

(4.7.21)

Combine Eqs. (4.7.20 & 4.7.21) to obtain pressure ratio across the expansion fan in terms of similarity parameter.

(4.7.22)

Further, the pressure coefficient across the expansion fan, may be expressed as a function of similarity parameter.

(4.7.23)

Multiply and divide the right-hand side by and simplify to obtain the following relation.

(4.7.24)

It may be seen that pressure coefficient for hypersonic shock and expansion wave, are related through the similarity parameter in the limit of hypersonic Mach numbers. Hence, the Eqs (4.7.19 & 4.7.24) are analogous.