Sarvajanik College of Engineering & Technology 1.Submitted To: Professor Vaishali Umrigar 2.Presented By: Mr. vivek kathiriya (22) Mr. kheni parth (23) Miss. koshiya dhruti (24) Mr. kothiya viren (25) Subject: Fluid flow Phenomena Branch: chemical engineering

HAGEN-POISEUILLE EQUATION.  For practical calculations Eq.(1) is transformed by eliminating tow in favor of deltaPs by the use of Eq.(2) and using pipe diameter in place of pipe radius. The result is Solving for delta Ps gives 3.

And since 4. Substiti tuning from eq.(4) into eq.a gives 5. Eq.(3) is the Hagen-Poiseuille equation. One of its uses is in the experimental measurement of viscosity,by measuring the pressure drop an volumetric flow rate through a tube of known length and diameter.From the flow rate,V bar is calculated by Eq.b and mue is calculated by Eq.(3) In practice, corrections for kinetic energy and entrance effects are necessary.

EFFECT OF ROUGHNESS  The discussion thus far has been restricted to smooth tubes without defining smoothness.  It has long been known that in turbulent flow a rough pipe leads to a larger fraction fracter for a given reynolds number than a smooth pipe does.  If a rough pipe is smoothed, the friction factor is reduced. When further smoothing brings about no further reduction in friction factor for a given Reynolds number the tube is said to be hydraulically smooth, Eq.c refers to a hydraulically smooth tube.

 Above Figure shows several idealized kinds of roughness. The height of a single unit of roughness is denoted by k and is called the roughness parameter.  From dimensional analysis, f is a function of both Re and the relative roughness k/D, where D is the diameter of the pipe.  For a given kind of roughness, e.g., that shown in Fig. a and b, it can be expected that a different curve of f versus Re would be found for each magnitude of the relative roughness and also that for other types of roughness, such as those shown in Fig.c and d, different family curve of Re versus f would be found for each type of roughness.  Experiments on artifically roughened pipe have confirmed these expectations.

 For design perposes, the friction charecteristics of round pipe, both smooth and rough, and summarized by the friction factor chart, which is a log-log plot of f versus Re for laminar flow eq.relates the friction factor to the reynolds no. A log-log plot of eq. Strat line with a slope of -1 this plot line is shown figure for reynolds no. Less than  For turbulant flow the lowest line represent the friction factor for smooth tube and is consistent with eq. A muchmore convenient empirical eq. For this line is the relation. 

 The other over curved lines in the turbulant flow rang represent the friction factor for verious types of commercial pipe, each of which is characterized by a different value of k.  For steel pipe and other rough pipes, the friction factor becomes independent of the Reynolds num. For Reynolds num. Greater than  For different flow regimes in a given system, the variation of pressure drop with flow rate can be found from eqn.  For laminar flow (Re<2100)  For turbulent flow (2500<Re< )  For very turbulent flow (Re> )

 The friction loss h from sudden expansion of cross section is propotional to the velocity head of the fluid in the small conduit and can be written.  where, Ke=expansion loss of coefficient  Va=average velocity

 Friction loss from sudden expansion of cross section   If cross section of pipe is suddenly enlarged,the fluid stream separates from the wall and issues as a jet in to the enlarged section. The jet then expand to fill the entire cross section of the large conduit. The space between the expanding jet and the conduit wall is filled with fluid in vertex motion characteristic of boundary layer sepration,and considerable friction is generated within this space. This effect is show in fig.

 The calculation utilizes the continuity eq.,the steady flow momentum balance eq.,and the bornoulli eq. consider the control volume defined by section AA and BB and the inner surface of the larger doenstream conduit between these section, as shown in fig. gravity forces do not appear because the pipe is horizontal, and wall friction is negligible because the wall is relatively short and there is almost no velocity gradient at the wall betweeen the section. The only forces,therefor, are pressure forces on section AA and BB. The momentum eq. given

 When the cross section of the conduit is suddenly reduced,the fluid stream can not follow around the sharp corner and the stream break contact with the wall of the conduit.A jet is formed, which flows into the stagnant fluid in the smaller cross section,and down stream from the point of contraction the normal velocity distribution eventually is reestablished. The cross section of minimum area at which the jet changes from a contraction to an expansion is called the vena contracta. The flow pattern of a sudden contraction is shown fig. section CC is drawn at the vena contracta. Vortices appear as shown in the fig.

 The friction loss of sudden contraction is proportional to the velocity head in smaller conduit and can be calculated by the eq. Where the proportionality factor Kc is called the contraction loss coefficient and Vb is the average velocity in the smaller,or downstream section, experimentlly, for laminar flow, Kc<0.1 and the contraction loss hfc is negligible.for turbulent flow, Sa and Sb are the cross sectional areas of the upstream and downstream conduits, respectively. When a liquid is discharged through a pipe welded to the wall of a large tank Sb/Sa is nearly zero and Kc=0.4.

 fitting and valves disturb the normal flow line and cause friction. In short lines with many fittings, the friction loss from the fittings may be greater then that from the straight pipe. The friction loss hff from fitting is found from an eq. similar to eq.  where Kf=loss factor for fitting Va=average velocity  Factor kf is found by experiment and differs for each type of connection. A short list of factors given in table.

 Thank you