Loss due to friction

E = Head loss due to friction in feet of flowing fluid... 

Within low-pressure operating ranges, the slight pressure loss due to friction in vapor pipes may mean an appreciable loss of total available temperature difference. 

While designers of fluid power equipment do what they can to minimize turbulence, it cannot be avoided. For example, in a 4-inch pipe at 68°F, flow becomes turbulent at velocities over approximately 6 inches per second (ips) or about 3 ips in a 6-inch pipe. These velocities are far below those commonly encountered in fluid power systems, where velocities of 5 feet per second (fps) and above are common. In laminar flow, losses due to friction increase directly with velocity. With turbulent flow, these losses increase much more rapidly. 

Equation 3.11 is due to Blasius(6) and the others are derived from considerations of velocity profile. In addition to the Moody friction factor / = 8R/pu2, the Fanning or Darcy friction factor / = 2R/pu2 is often used. It is extremely important therefore to be clear about the exact definition of the friction factor when using this term in calculating head losses due to friction. 

To calculate —APf it is therefore necessary to evaluate e/d and obtain the corresponding value of

head loss due to friction hf as ... 

With the friction factors used by Moody and Fanning, / and / respectively, the head loss due to friction is obtained from the following equations ... 

The dynamic loss due to friction in the pipe, the miscellaneous losses, and the pressure loss through equipment. 

Viscosity is the property of a fluid that offers resistance to the relative motion of fluid molecules. The energy loss due to friction in a flowing fluid is due to its viscosity. 

A large tank containing water has a 51 mm diameter hole in the bottom. When the depth of the water is 15 m above the hole, the flow rate through the hole is found to be 0.0324 m3/s. What is the head loss due to friction in the hole ... 

Pumps are devices for supplying energy or head to a flowing liquid in order to overcome head losses due to friction and also, if necessary, to raise the liquid to a higher level. The head imparted to a flowing liquid by a pump is known as the total head Ah. If a pump is placed between points 1 and 2 in a pipeline, the heads for steady flow are related by equation 1.14... 

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. 

In equation 4.2, hfs is the head loss due to friction, zs is the static head and Ps is the gas pressure above the liquid in the tank on the suction side of the pump. If the liquid level on the suction side is below the centre-line of the pump, zs is negative. 

An incompressible fluid flows upwards in steady state in a cylindrical pipe at an angle 8 with the horizontal. Assume that the head loss due to friction is negligible. 

Knowledge of the sample pressure is essential in all high-pressure experiments. It is vital for determinations of equations of state, for comparisons with other experimental studies and for comparisons with theoretical calculations. Unfortunately, one cannot determine the sample pressure directly from the applied force on the anvils and their cross-sectional area, as losses due to friction and elastic deformation cannot be accurately accounted for. While an absolute pressure scale can be obtained from the volume and compressibility, by integration of the bulk modulus [109], the most commonly-employed methods to determine pressures in crystallographic experiments are to use a luminescent pressure sensor, or the known equation of state of a calibrant placed into the sample chamber with the sample. W.B. Holzapfel has recently reviewed both fluorescence and calibrant data with the aim of realising a practical pressure scale to 300 GPa [138]. 

APs = pressure loss due to friction in unit length of the pipe for solvent alone APa = pressure loss due to friction in unit length of the pipe for the solution containing the additive... 

Having introduced f, the objective is now to find a convenient analogy with which we may calculate any/factor. But first, how is this factor to be applied Why not just use the simple term hL and be done In answer, the hL factor, if reviewed in Fig. 6.1, is actually a part of the hydraulic grade line factor 144 Pi/p. Thus, the correct thing to do here is to put it in this factor. In all equation relationships of fluid flow problem solving, this is done. This simply says that/represents the flow of fluid losses due to friction inside pipe in all equations used. 

Step 1. For pressure loss due to friction, first determine the homogeneous flow liquid ratio X, volume of liquid per volume of mixed fluid flow. 

Here A/jf is the head loss due to friction and is directly related to the pressure loss due to friction A/ f by A/ f = pgAhf. 

Therefore, the total pressure or head loss due to friction in pipework due to the pipe and fittings is given by... 

In equation 6.33, if there were no losses, the coefficient of discharge of the meter would be unity, and for a flowrate G the loss in head would be (hv — hf) where hf is the head loss due to friction. 

The roughness of the pipe affects the ratio e/d. The rougher the pipe surface, the higher will be e/d and there will be an increase in R/pu2. This will increase the head loss due to friction and will ultimately increase the power required. 

---