Air flows through a venturi and into the atmosphere. Air density is ρ; atmospheric pressure is ′Pa′; throat diameter is ′Dt′ exit diameter is ′D′, and exit velocity is U. the throat is connected to a cylinder containing a frictionless piston attached to a spring. The spring constant is ′k′. the bottom surface of the piston is exposed to the atmosphere. Due to the flow, the piston moves by distance x. assuming incompressible frictionless flow, x is ____

A. (ρU^2 /2)πDs^2 B. (ρU^2/8k)(D^2/Dt^2 −1)πDs^2 C. (ρU^2/2k)(D^2/Dt^2 −1)πDs^2 D. (ρU^2/8k)(D^4/Dt^4 −1)πDs^2