Smooth pipes estimating flow

Estimate the value of the eddy kinematic viscosity s as a function of position for turbulent flow of water in a smooth pipe of internal diameter 100 mm. The centre-line velocity is 6.1 m/s and the pressure drop over a... 

For Newtonian fluids flowing in smooth pipes, the friction losses can be estimated for laminar flow (Re < 2100) using the Fanning friction factor, f. The Reynolds number, Re, is given by ... 

For turbulent flow (2100 < / e < 100,000) in long, smooth pipes, the Blasius formula may be used to estimate the friction factor ... 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

This is a very high pressure drop, even though the packed bed is very shallow For comparison purposes, let us estimate the pressure drop for the wetted-wall column of Example 2.12. To estimate the pressure drop in turbulent flow through a circular smooth pipe of diameter D and length Z (Welty et al., 1984),... 

Water at a temperature of 20°C is flowing through a smooth pipe of internal diameter 0-2 m. The pressure drop over a horizontal test section of length 305 m is measured as 0-21 x 10 Pa. Estimate the flowrate. (Density of water at 20°C = 988kgm , viscosity = 10 Pas.)... 

One of the simplest approaches to quantify the pressure field downstream of the constriction used to generate cavitation is to assume linear pressure recovery profile. Yan et al. [8] have used similar approach also considering a single bubble to be existing independent of the other bubbles. Such an approach may be adequate when the intensity of turbulence is quite low i.e. for a venturi type constriction or any other constriction with a smooth variation in the cross-sectional flow area. The pressure recovery from the point at which cavitation starts to any downstream pipe position can be approximated by a linear expression with respect to the distance downstream of the constriction. In such a case, the local pressure at any downstream position can be estimated as ... 

The Reynolds number characterizing laminar-turbulent transition for bulk flow in a pipe is about Re 2300 provided that the fluid moves unidirectionally, the pipe walls are even and behave in a hydraulically smooth manner, and the internal diameter remains constant. However, intestinal walls do not fulfill these hydraulic criteria due to the presence of curvatures, villi, and folds of mucous membrane, which are up to 8 mm in the duodenum, for instance (Fig. 18). Furthermore, the internal diameter of the small intestine is estimated to... 

There are insnfficient data in the literatnre to provide a reliable estimate of the effect of roughness on friction loss for non-Newtonian flnids in tnrbnlent flow. However, the influence of roughness is normally neglected, since the laminar bonndary layer thickness for such fluids is typically much larger than for Newtonian fluids (i.e., the flow conditions most often fall in the hydraulically smooth range for common pipe materials). An expression by Darby et al. (1992) for / for the power law flnid, which applies to both laminar and turbulent flow, is... 

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