Friction pressure loss turbulent flow

The flow changes from laminar to turbulent in the range of Reynolds numbers from 2,100 to 4,000 [60]. In laminar flow, the friction pressure losses are proportional to the average flow velocity. In turbulent flow, the losses are proportional to the velocity to a power ranging from 1.7 to 2.0. 

A typical flow rate of 2 m3/min in the drill pipe (diameter = 0.1 m) gives a fluid velocity of 4.2 m/s, which causes fully turbulent flow in most drilling fluids. The calculation of the pressure drop down the length of the drill pipe is made somewhat complex by the flow being turbulent and the non-Newtonian rheology of the drilling fluid. These calculations are, however, important as about 30% of the total frictional pressure losses occur in the drill pipe. 

Figures 28a and 28b compare the measured and calculated frictional pressure losses for laminar and turbulent flow of the drilling fluid through...

Annulus. From the drill pipe, the drilling fluid is jetted out of the bit nozzles and into the annulus. The jets are designed to remove drilled cuttings away from the drill bit. The pressure drop across the nozzles accounts for about 60% of the total frictional pressures losses during the circulation of the drilling fluid. About 90% of the pressure drop across the nozzles is due to the turbulence at the outlet, with only about 10% due to the flow through the nozzles. 

To extend the prediction of vs to flow regimes where Rec 0.1 it is necessary to use empirical correlations between Rec and a friction factor, similar to the approach used for calculating frictional pressure losses in turbulent pipe flow. The cutting friction factor/ is defined by... 

Skin friction loss. Skin friction loss is the loss from the shear forces on the impeller wall caused by turbulent friction. This loss is determined by considering the flow as an equivalent circular cross section with a hydraulic diameter. The loss is then computed based on well-known pipe flow pressure loss equations. 

Laminar flow after transition usually turns into turbulent flow when Re > 2000. It has been shown that the pressure loss of a turbulent flow is caused by a friction factor with the magnitude of... 

System components, such as pumps, valves and gauges, create both turbulent flow and high friction components. Pressure drop, or a loss of pressure, is created by a combination of turbulent flow and friction as the fluid flows through the unit. System components that are designed to provide minimum interruption of flow and pressure should be selected for the system. 

While friction increases markedly for sharper curves than this, it also tends to increase up to a certain point for gentler curves. The increases in friction in a bend with a radius of more than 3 pipe diameters result from increased turbulence near the outside edges of the flow. Particles of fluid must travel a longer distance in making the change in direction. When the radius of the bend is less than 2 pipe diameters, the increased pressure loss is due to the abrupt change in the direction of flow, especially for particles near the inside edge of the flow. 

The pressure is given at the connection of the nozzle to the pipe so this will be taken as location 1. The flow is caused by the fact that this pressure is greater than the pressure of the atmosphere into which the jet discharges. The pressure in the jet at the exit from the nozzle will be very nearly the same as the atmospheric pressure so the exit plane can be taken as location 2. (Note that when a liquid discharges into another liquid the flow is much more complicated and there are large frictional losses.) Friction is negligible in a short tapering nozzle. The nozzle is horizontal so Z = z2 and for turbulent flow a = 1.0. With these simplifications and the fact... 

In equation 1.14, z, P/(pg), and u2/(2ga) are the static, pressure and velocity heads respectively and hf is the head loss due to friction. The dimensionless velocity distribution factor a is for laminar flow and approximately 1 for turbulent flow. 

The pressure drop across the cyclone is an important parameter in the evaluation of cyclone performance. It is a measure of the amount of work that is required to operate the cyclone at given conditions, which is important for operational and economical reasons. The total pressure drop over a cyclone consists of losses at the inlet, outlet and within the cyclone body. The main part of the pressure drop, i.e. about 80%, is considered to be pressure losses inside the cyclone due to the energy dissipation by the viscous stress of the turbulent rotational flow [9], The remaining 20% of the pressure drop are caused by the contraction of the fluid flow at the outlet, expansion at the inlet and by fluid friction on the cyclone wall surface. 

We see that Apjl, the frictional pressure drop per unit depth of bed, is made up of two components. The first term on the right-hand-side accounts for viscous (laminar) frictional losses, cc pu. and dominates at low Reynolds numbers. The second term on the right-hand-side accounts for the inertial (turbulent) frictional losses, oc pu2, and dominates at high Reynolds numbers. For further information about flow through packed beds, see Chapter 7 An Introduction to Particle Systems . 

Related Calculations. Helical Coils. The same procedure can be used to calculate the pressure drop in helical coils. For turbulent flow, a friction factor for curved flow is substituted for the friction factor for straight tubes. For laminar flow, the friction loss for a curved tube is expressed as an equivalent length of straight tube and the friction factor for straight tubes is used. The Reynolds number required for turbulent flow is 2100[1 + 12(Dj/Dc)1/2], where Dt is the inside diameter of the tube and Dc is the coil diameter. 

Construct the dry-pressure-drop line on log-log coordinates (optional). For turbulent flow, the gas-phase pressure drop for frictional loss, contraction and expansion loss, and directional change loss are all proportional to the square of the superficial F factor. For the dry packing the pressure drop can be calculated from the equation... 

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... 

Solving problems in chemical engineering and science often requires finding the real root of a single nonlinear equation. Examples of such computations are in fluid flow, where pressure loss of an incompressible turbulent fluid is evaluated. The Colebrook [8] implicit equation for the Darcy friction factor, f, for turbulent flow is expressed... 

Several studies have been reported to determine friction losses in turbulent flow of slurries. Hannah et al. (29) presented an approach in which they compared expressions for the friction pressure of the slurry and clean fluid. In their analysis, they assumed Blasius (30) turbulent Fanning friction factor versus Reynolds number equation for Newtonian fluids. The following expression for estimating slurry friction pressure knowing the clean fluid friction pressure is proposed. 

We are no more able to calculate the pressure drop in steady, turbulent flow in a noncircular conduit than we are in a circular one. However, it seems reasonable to expect that we could use the friction-loss results for circular pipes to estimate the results for other shapes. Let us assume that the shear stress at the wall of any conduit is the same for a given average fluid flow velocity independent of the shape of the conduit. Then, from a force balance on a horizontal section like that leading to Eq. 6.3, we conclude that in steady flow... 

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