Smooth pipe turbulent flow

More complex equations have been developed for the flow of power-law fluids under turbulent flow in pipes [85,86,90], The foregoing applies to smooth pipes. Surface roughness has little effect on the friction factor for laminar flow, but can have a significant effect when there is turbulent flow [85],... 

C. F. Colebrook. Turbulent flow in Pipes, with Particular Reference to the Transition between the Smooth and Rcjhgh Pipe Laws. Journal of the Institute of Civil Engineers London. 11 (1939), pp. 133-156. 

Colebrook CF (1939) Turbulent Flow in Pipes, with particular reference to the Transition Region between Smooth and Rough Pipe Laws. J Inst Civ Eng 12(4) 133-156... 

C. F. Colebrook, Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws, J. Inst. Civ. Eng. 11 133-155 (1938-9). 

Turbulent flow in pipes, where 1 is replaced by the mean pipe diameter D, can occur when the Reynolds number exceeds 2000. Empirical equations have been established for turbulent flow of Newtonian materials [51,52]. For smooth pipes. 

For laminar flow (Re < 2000), generally found only in circuits handling heavy oils or other viscous fluids, / = 16/Re. For turbulent flow, the friction factor is dependent on the relative roughness of the pipe and on the Reynolds number. An approximation of the Fanning friction factor for turbulent flow in smooth pipes, reasonably good up to Re = 150,000, is given by / = (0.079)/(4i e ). 

In laminar flow,/is independent of /D. In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydrauhcaUy smooth flow). For greater Reynolds numbers,/deviates from the smooth pipe cui ve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. The Reynolds number above which / becomes essentially independent of Re is (Davies, Turbulence Phenomena, Academic, New York, 1972, p. 37) 20[3.2-2.46ln( /D) ... 

Fluid flow is also critical for proper operation of a hydraulic system. Turbulent flow should be avoided as much as possible. Clean, smooth pipe or tubing should be used to provide laminar flow and the lowest friction possible within the system. Sharp, close radius bends and sudden changes in cross-sectional area are avoided. 

HARTNETT and KOSTIC 26 have recently examined the published correlations for turbulent flow of shear-thinning power-law fluids in pipes and in non-circular ducts, and have concluded that, for smooth pipes, Dodge and Metzner S(27) modification of equation 3.11 (to which it reduces for Newtonian fluids) is the most satisfactory. 

The right-hand side of equation 10.224 gives numerical values which are very close to those obtained from the Blasius equation for the friction factor (j> for the turbulent flow of a fluid through a smooth pipe at Reynolds numbers up to about 106. 

For hydrodynamically smooth pipes, through which fluid is flowing under turbulent conditions, the shear stress is given approximately by the Blasius equation ... 

For flow in a smooth pipe, the friction factor for turbulent flow is given approximately by the Blasius equation and is proportional to the Reynolds number (and hence the velocity) raised to a power of -2. From equations 12.102 and 12.103, therefore, the heat and mass transfer coefficients are both proportional to w 75. 

Derive an expression relating the pressure drop for the turbulent flow of a fluid in a pipe to the heat transfer coefficient at the walls on the basis of the simple Reynolds analogy. Indicate the assumptions which are made and the conditions under which you would expect it to apply closely. Air at 320 K and atmospheric pressure is flowing through a smooth pipe of 50 mm internal diameter, and the pressure drop over a 4 m length is found to be 150 mm water gauge. By how much would you expect the air temperature to fall over the first metre if the. wall temperature there is 290 K ... 

Derive the relation between the friction factor and Reynolds number in turbulent flow for smooth pipe [Eq. (6-34)], starting with the von Karman equation for the velocity distribution in the turbulent boundary layer [Eq. (6-26)]. 

A coal slurry is found to behave as a power law fluid, with a flow index of 0.3, a specific gravity of 1.5. and an apparent viscosity of 70 cP at a shear rate of 100 s 1. What volumetric flow rate of this fluid would be required to reach turbulent flow in a 1/2 in. ID smooth pipe that is 15 ft long What is the pressure drop in the pipe (in psi) under these conditions ... 

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... 

Considerable effort has been expended in trying to And algebraic expressions to relate/to Re and eld,. For turbulent flow in smooth pipes, the simplest expression is the Blasius equation ... 

The most widely accepted relationship for turbulent flow in smooth pipes is the von Karman equation... 

Equation 2.69 fits the experimental data for turbulent flow in smooth pipes of circular cross section for y+ > 30 when 1 IK and C are given the values 2.5 and 5.5 ... 

Friction factors for turbulent flow in smooth pipes... 

Experimental results for the Fanning friction factor for turbulent flow of shear thinning fluids in smooth pipes have been correlated by Dodge and Metzner (1959) as a generalized form of the von Karman equation ... 

A centrifugal pump is used to pump a liquid in steady turbulent flow through a smooth pipe from one tank to another. Develop an expression for the system total head A/t in terms of the static heads on the discharge and suction sides zd and zs respectively, the gas pressures above the tanks on the discharge and suction sides Pd and Ps respectively, the liquid density p, the liquid dynamic viscosity p, the gravitational acceleration g, the total equivalent lengths on... 

Figure 7.4 Representations of hydrodynamic flow, showing (a) laminar flow through a smooth pipe and (b) turbulent flow, e.g. as caused by an obstruction to movement in the pipe. The length of each arrow represents the velocity of the increment of solution. Notice in (a) how the flow front is curved (known as Poiseuille flow ), and in (b) how a solution can have both laminar and turbulent portions, with the greater pressure of solution flow adjacent to the obstruction.

The opening of the test pipe has been designed and tested to ensure fully developed turbulent flow in the test section. Hence, the inlet length of the pipe to the first pressure gap amounts to 220 x d. The device has been carfully tested and calibrated with water, which complies with the Newtonian theory of fluids for smooth pipes. Measurements are taken after stabilization occurs and then a magnetic device in the form of a swinging arm turns the outlet tube to the collecting vessel and at this moment a stop-watch is... 

However, the flow regime of a film cannot be defined uniquely as laminar or turbulent, as in the case of pipe flow, due to the presence of the free surface. Depending on the values of AFr and JVw , the free surface may be smooth, or covered with gravity waves or capillary or mixed capillary-gravity waves of various types. Thus, under suitable conditions, it is possible to have smooth laminar flow, wavy laminar or turbulent flow, where the wavy flows may be subdivided into gravity or capillary... 

For turbulent flow of Newtonian fluids in smooth pipes, two common correlations are those of Blasius [413] for 3000 < Re < 100 000 ... 

In the turbulent flow range, which appears in industrially rough (= smooth) pipes at Re > 106, the following applies ... 

---