## 1 Introduction
[PERSON] and [PERSON] [17] used differential pressure readings in a vertically installed venturi meter to identify the flow regime based on wavelet transform method. The method processes raw differential pressure signals by decomposition of these signals into several standard forms and correlates them to the energy levels and flow pattern. [PERSON] [20] used a high frequency pressure transducer (Validype DP15 at 5 kHz with a cutoff frequency of 20 Hz) to measure the differential pressure signature in annular ducts for developing an approach to identify different flow regimes. The approach is based on three important parameters, dominant frequency (\(f_{\mathrm{d}}\)), which is the higher energy frequency of power spectral density (PSD); mode of PDF, called P\({}_{\mathrm{peak}}\): and the difference between maximum value and mode, called the dispersion measurement (\(\delta\)). [PERSON] et al. [21] studied horizontal two-phase flow in a rectangular section and developed a flow pattern map with the help of visual observations and dynamic pressure. A comparison of the resulting flow map was made against the flow regime maps for circular pipes, capillaries, and large rectangular geometries. It was concluded that no quantitative agreement exists, and hence the same flow map cannot be applied to different geometries. Later, [PERSON] et al. [22] further processed this data using tools like power spectral density function (PSD), pseudo-phase-plane trajectory, autocorrelation function, fractal dimensions, and Lyapunov exponents. Again, the data can be used for flow map development in rectangular sections but was not applicable for circular pipes. Another study [23] used a technique based on processing of differential pressure signals using Hilbert Huang transform (HHT) to differentiate between different flow regimes. Hilbert Huang transform was used to decompose signals into intrinsic mode functions (IMFs). The rules to identify different flow regimes were summarized from calculated energy fraction of IMFs and the mean residual value of functions. This method shows high precision in the case of slug and bubbly flow identification. [PERSON] [16; 24] used differential pressure data of nitrogen-water flow in vertically oriented pipe and observed that the shape of PDF can be used as a differentiating factor for different flow patterns. [PERSON] et al. [18] further modified and generalized the methodology used by [PERSON] [16; 24]. A signal processing approach was presented by using differential pressure measurements in slightly inclined annular ducts to characterize slug flow. A relation was established between differential pressure signals and void pressure waves, which has the potential to identify and characterize flow patterns. [PERSON] et al. [25] used differential pressure signals in gas-water two-phase flow in a vertical pipe and defined a flow pattern/regime identification technique by using magnitude and dominant frequency of FFT and magnitude and location of the PDF combined with artificial neural network. [PERSON] and [PERSON] [26] applied the elastic map algorithm and PDF of the normalized differential pressure in gas-water two-phase flow in an upwards vertical pipe to identify the flow regime. They concluded that the PDF of differential pressure is a reliable and strong indicator for flow regime identification. The elastic map method used is accurate and versatile and it can be automated. They postulated that the PDF of differential pressure signals can also be utilized to identify two-phase flow patterns in a horizontal pipe. In fact, the use of differential pressure fluctuations can be traced back to the original work of [PERSON] and [PERSON] [27], where parameter \(X\), is defined as:  
\[X=\sqrt{\frac{\left(dp/dz\right)_{g}}{\left(dp/dz\right)_{l}}} \tag{1}\]  
The focus of the published literature is on using differential pressure signals in vertical pipes to identify the flow regime. It is known that differential pressure is basically another term for pressure difference over a certain fixed length of pipe.