Ram pressure in astronomy and engineering

The ram pressure of a moving fluid, P_r, is the rise in pressure at a stagnation point relative to the upstream pressure. In astronomy, it is used to calculate the interaction of stellar winds with planets and to quantify the effects of ram pressure stripping. On aeroplanes and in wind tunnels, it is measured with a pitot-static tube, an inexpensive device with no moving parts that was invented in 1732. Up through the mid-1960s, across both astronomy and engineering the ram pressure of a moving gas and its momentum flux, ρ u², where ρ and u are the upstream mass density and flow speed, were properly treated as related but distinct quantities. This relationship may be expressed as P_r=Sp ρ u², where Sp is the dimensionless Spreiter number, which ranges between 0.5 and 0.88 for a monatomic gas, depending on the upstream Mach number, Ma . Unfortunately, by the early 1970s, in astronomy ram pressure was defined to be the momentum flux and Sp was fixed to be unity and forgotten as a parameter. This article seeks to raise awareness of this issue, and to review the determination of Sp for subsonic and supersonic flow.