# Homework 4

CM3110 Transport Processes I

# CM3110

1. Show for Newtonian fluids in laminar flow that the Fanning friction factor, f, is given by f=16/Re, where Re is the Reynolds number. SOLUTION
2. (Calculate flow rate from pressure drop - tube flow) For a pipe (inner diameter = 2.00 in) water at 25oC (density = 62.4 lbm/ft3, viscosity = 6.7197 X 10-4 lbm/(ft s)) is made to flow under a pressure drop per unit length of 1.90 X 10-2psi/in.  What will be the average velocity of the water in the pipe?  Is the flow laminar or turbulent? What would the pressure drop need to be for the flow to change from laminar to fully turbulent (or from turbulent to laminar, whichever is appropriate)? SOLUTION METHOD ONE. Also I solved it a second, similar way: ALTERNATE SOLUTION METHOD
3. (Macroscopic momentum balance - Tube flow) Using our nomenclature for doing macroscopic momentum balances, calculate the force on the walls for steady, turbulent flow of an incompressible newtonian fluid through a straight pipe.  Assume that the flow is downward, i.e. in the direction of gravity.  Note that the answer obtained is the same as performing a force balance, which we did when calclating the relationship between pressure and friction factor (see lecture 10).  SOLUTION
4. (Flow through an expanding bend) Geankoplis, 3rd edition, 2.8-4, page 110 Water at a steady state flow rate of 0.050 m3/s is flowing through an expanding bend that changes direction by 60o.  The upstream diameter is 0.0762 m and the downstream diameter is 0.2112m.  The upstream pressure is 68.94 kPa (gage pressure).  Calculate the downstream pressure and the vector force on the bend.  The entire apparatus is at 298K and you may neglect energy losses in the bend. SOLUTION
5. (Force on a U-Tube) Bird, Stewart, and Lightfoot, Transport Phenomena (Wiley, 1960) plm 7.D1.  Water is flowing in a horizontal, U-shaped tube.  The flow is turbulent, the inner diameter of the tube is 4.00 in, and the fluid is water at 68.0oF (density = 62.4 lbm/ft3, viscosity = 1.00 cP, flow rate = 3.00 ft3/s).  The pressure at surface "1" is 21 psia, and the pressure at surface "2" is 19 psia.  What is the total force on the bend?  SOLUTION
6. (Flow in noncircular conduits)The frictional losses in non-circular conduits are found to follow the same data correlations (friction factor versus Reynolds number) as flow through circular conduits if the equivalent hydrodynamic diameter DH is used instead of the regular pipe diameter D both in the definitions of Re and of Fanning friction factor (See Geankoplis 3rd edition p99 or Denn or Perry's Handbook).  DH , which is equal to four times the hydraulic radius RH (weird, but true), is equal to four times the ratio of (cross-sectional area of the conduit) to (wetted perimeter of the conduit).  Calculate the equivalent hydraulic diameter for an annular conduit with inside diameter D1 and outside diameter D2.  Calculate the equivalent hydraulic diameter for a rectangular duct of sides a and b.  What is the pressure-drop per unit length for room-temperature water flowing at 3 ft3/s in an annular conduit?  The inner diameter is 2.0 inches, and the outer diameter is 5.0 inches. SOLUTION