. The flow is driven by a periodic, time-dependent pressure gradient:
𝜕u𝜕y=U∞f′′(η)𝜕η𝜕y=U∞f′′(η)U∞νxpartial u over partial y end-fraction equals cap U sub infinity end-sub f double prime of open paren eta close paren partial eta over partial y end-fraction equals cap U sub infinity end-sub f double prime of open paren eta close paren the square root of the fraction with numerator cap U sub infinity end-sub and denominator nu x end-fraction end-root advanced fluid mechanics problems and solutions
tanθ=2cotβ[M12sin2β−1M12(γ+cos2β)+2]tangent theta equals 2 cotangent beta open bracket the fraction with numerator cap M sub 1 squared sine squared beta minus 1 and denominator cap M sub 1 squared open paren gamma plus cosine 2 beta close paren plus 2 end-fraction close bracket advanced fluid mechanics problems and solutions