By means of detrending moving average and rescaled range analysis, the multifractal characteristics of the pressure fluctuation rate series (PFRS) derived from instantaneous fluctuations signals (PFS) in circulating jet tank (CJT) were investigated and the criteria of different scales were established. The central parts of the probability density functions of PFRS were exponentially distributed, and the positive part decayed slower than the negative part. The existence of multifractal characteristics of PFRS under different circumferential angles had been confirmed by both the strong q-dependence of generalised Hurst exponents and continuous wavelet decompositions. The high frequency Hurst exponents based on rescaled range analysis were all >0.66 with the changing Re, which presented that PFRS had the long-range dependence and aperiodicity. The local fractal dimensions declined with the increasing scales and presented the same trend at different dimensionless radial positions r/R0. The decomposed fluctuation components at scale a = 1–4 had different local fractal dimensions which revealed that the fluid flow was more complicated. The fluctuation energy profiles of PFRS indicated that the instantaneous pressure fluctuations were dominated by the interaction between macro-scale vortexes and liquid phase.