Fig. 2: Two types of dynamic pressure and their probability density spectra.

All measurements of dynamic pressure shown in this figure are obtained at the location of 3.35 m from impact at a height 0.45 m above the flow base. a Variation of the entire dynamic pressure P_dyn as a function of time as recorded by piezoelectric sensor and the corresponding probability density function shown in b. The pressure signal of P_dyn shows abundant near-instantaneous high-pressure peaks of several hundreds to thousands of Pascal, which are characterized by pressure increases in less than one millisecond. The inset highlights an example of one of the near-instantaneous high-pressure signals, which are associated with impacts from individual particles with the pressure sensor. c Variation of the partial dynamic pressure signal P_impact as a function of time recorded by the piezoelectric sensor, which shows only those parts of the entire pressure signal P_dyn that are associated with near-instantaneous pressure peaks. d The probability density function of P_impact. e Variation of the partial dynamic pressure signal P_{dusty gas} as a function of time, which is the dynamic pressure of the continuous dusty gas phase computed as the difference between P_dyn(t) and P_impact(t) via Eq. (2). The black line shows a 20-millisecond average of the timeseries P_{dusty gas} (depicted in blue) The orange line shows the corresponding timeseries of the dynamic pressure P_Bernoulli, computed independently from timeseries of flow velocity and flow density via Eq. (1). f probability density functions of P_{dusty gas} (blue) and P_Bernoulli (orange).