The reservoir core sample shown in Figure 1 has a permeability of 1 Darcy. What does this mean? Figure 1

10. Explain the principle of hydraulic diameter and its use for ducts with non-circular cross-sections.

4. Consider two-dimensional, laminar, unidirectional flow between parallel (spacing: 2h), vertical plates. One plate, to the left, is moving downward with constant velocity vi; the other is moving upward at a constant velocity v2. If we consider the fluid Newtonian, solve for the velocity profile using our newly defined Navier-Stokes Eqns.

5. The surface tension of water at 20°C in a 2mm diameter tube is equal to 0.075 N/m. For a water- glass interface, determine the capillary rise in the tube in mm. !

The laminar flow of water in a small pipe is given by where R = 0.5 cm is the pipe radius, and Umax = 20 cm/s. Assume the temperature is 15°C. (a) Find the wall shear stress. (b) Find the pressure drop in a 10 cm length of the pipe. (c) Verify that the flow is indeed laminar.  

For laminar flow, can expressions for the mass-transfer coefficient be determined from theory using Fick’s law? If so, how?

A Newtonian liquid with constant density and viscosity is flowing under laminar conditions inside a horizontal circular pipe with inside diameter of D. The length of pipe is L and the pressure at entrance is P0 while it is PL at exit. After exact formulation of this problem obtain the velocity profile, its maximum, average and ratio between the average and maximum velocities

As shown in the accompanying figure, a thin flat plate rests on top of a film of ambient temperature (i.e. 20 °C) water. When a small force F is applied to this plate, the velocity profile within the water film can be described as vx = 40y-800y² where y is the distance (m) from the bottom stationary plate. a. Show that velocity equation satisfies the 'no-slip' conditions that must exist for both the top moving plate and bottom stationary plate. b. Calculate the magnitude of the shear stress (in Pa) that is acting on the top plate 10 mm 0.32 m/s -X

5

express in 4 decimal places    ans asap