By P. Skalle
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4) when expressed in Cartesian coordinates. 5) 4. 6) Expressed in cylindrical coordinates the eqn. of motion (only the axial component (x-direction) is of interest) for steady state, constant density and constant viscosity yields: 0=− 1 ∂ ∂ 1 ∂ 2vx ∂p ∂2 + m + rg x r − v x + 2 v x + 2 2 ∂x ∂ ∂ r r r ∂ ∂ q x r Both ∂p and ∂vx are negative since ∂p and ∂v decreases for increasing x and r values respectivley. ∂x ∂r 5. Energy equation or law of conservation of energy is interesting only for problems involving temperature change.
17) presented graphically. 21) is known as the Hagen-Poiseuille equation for laminar pipe flow. The pressure loss Dp is due to viscous stress only, and is linearly proportional to flow rate or average velocity and to length of pipe. For the Bingham model (and Power law model) the procedure is identical, only boundary conditions are different as indicated in Figure 4-4. R r ro vo Figure 4-4: Flow profile for laminar flow of a fluid obeying the Bingham rheology model. 6) by using t = ty at r = ro.
2 m long pipe leading to the nozzles. Since the nozzle velocity is much larger than the velocity at the entrance and at the outlet, the effect of ignoring entrance and end effect plus friction through the nozzle-pipe are compensated by including them in the loss coefficient, Kbit. 0 (the losses at the entrance are small due to the ellipsoidal shape of the entrance). 0. 11. 52 Drilling Fluid Engineering Hydraulic friction in the circulating system However, the uncertainty of estimating pressure loss through bit nozzles is high.