Friction Factors for Turbulent Flow in Curved Pipes

Abstract

The object of this paper is to furnish the engineer with reliable data on the friction factors to be used in computing the pressure losses for turbulent flow in smooth curved pipes. The empirical formulas proposed, backed by theoretical considerations, appear to define the influence of curvature upon the law of resistance with satisfactory accuracy.

Development of experimental heat transfer correlations using Newtonian fluids in helical coils

“…It may be pointed out that any Reynolds number is not in a position to reveal the flow pattern such as laminar, transition and turbulent in helical coils. Out of all the correlations available in the literature for critical Reynolds number, correlation developed by Mujawar and Rao [17] when tested with published correlations, gives close results with Ito [18] and Schmidt [19] for any practical coil curvature ratios which is of practical interest, Pawar and Sunnapwar [30]. Correlations developed for calculating critical Reynolds number by other authors Ito [18], Kubair and Varrier [20], Schmidt [19], Srinivasan et al [21], Ito [22], and Cioncolini and Santini [23] are applicable for Newtonian fluids only whereas equation developed by Mujawar and Rao [17] is applicable to Newtonian as well as for non-Newtonian fluids, is significant.…”

“…The flow rate of cold water through the test section was adjusted by a bypass line to get mass flow rate in the range of 0.0338-0.1031 kg/s. This corresponds to a laminar flow regime with Reynolds number in the range of 3166-9658 as per criteria defined by Mujawar and Rao [17] and Ito [18]. From present modified Type-III…”

A numerical study of the similarity of fully developed laminar flows in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio

“…For example, Trefethen (1957) showed that variation in the friction factor due to the secondary flow patterns in both rotating and curved pipes can be expressed in terms of the Reynolds number and a dimensionless parameter characterizing each flow, but he did not provide a theoretical explanation. Ito and Nanbu (1971) and Ito (1959) derived dimensionless parameters for these flows using an integral method, but they did not mention any relationships between these parameters. Ishigaki (1994) introduced the dimensionless parameters to demonstrate the quantitative analogy between two flows in a circular pipe, and obtained satisfactory results.…”

An experimental study on swirling flow in a 90 degree circular tube by using particle image velocimetry

“…Dean also conducted experiments on a fully developed laminar flow from a bent tube with weak bending, and the results were compared with the simple Navier-Stokes formula. Ito (1959) manufactured bent tubes with a relative radius of Rc = 1.25 a 14.6 using brass castings and conducted experiments on the pressure drop of turbulent flows. Through these experiments, results were compared with those of Eustice and Dean and with consideration of further practical aspects.…”