Fluid Mechanics

When a fluid flows in a conduit, there is friction between the flowing fluid and the pipe walls. The result of this friction is a net loss of energy in the flowing fluid. The fluid pressure is the source of the energy loss. Thus, whenever a fluid flows through a pipe, the pressure of the fluid will decrease in the direction of the flow in the absence of other effects, such as a gravitationalfield, or mechanical devices, such as pumps. Fluid flow can be laminar or turbulent in nature. Turbulent flow is characterized by intense mixing phenomena often observed as eddies within the flow field. Laminar flow is characterizedby a very smooth appearance and is devoid of intense missing phenomena. The third regime of fluid flow is transitional. As the name implies, it occurs when the fluid flow is in transition from laminar to turbulent flow or from turbulent to laminar flow. In general, the flow is considered to be laminar below Re-2000 and turbulent above Re-3000.

For the pump curve provided: suppose we want to pump water at 120 gpm and with a 40ft head

A relationship often used to model flow in porous media is Darcy's law. Where k is the Darcy permeasbility

A tank contains 9 kg of CO₂ at 20°C and 2.0 MPa. Estimate the volume of the tank, in m³.

An amazing number of commercial and laboratory devices have been developed to measure fluid viscosity, as described in Ref. 29 and 49. Consider a concentric shaft, fixed axially and rotated inside the sleeve. Let the inner and outer cylinders have radii ri and ro, respectively, with total sleeve length L. Let the rotational rate be 2 (rad/s) and the applied torque be M. Using these parameters, derive a theoretical relation for the viscosity of the fluid between the cylinders.

(a) Prove that both of these formulas are dimensionally homogeneous. (b) Suppose that a 2.5 mm diameter aluminum sphere (density 2700 kg/m³) falls in an oil of density 875 kg/m³. If the time to fall 50 cm is 32 s. estimate the oil viscosity and verify that the inequality is valid.

Determine the manometer reading h if density of oil is po = 800 kg/m3 density of water is P

2) Determine the nondimensional relationship between the drag force Fo and μ (viscosity), v (velocity), p (density), D (diameter of sphere). (Hint: Fo and μ each appear in only one dimensionless group).

2. Find the magnitudes and locations of the lines of action of the horizontal and vertical components of the force exerted by the water at rest on wall segment ABC for the tank illustrated below. Take r = 6 ft and h = 10 ft, and the width of the tank (into the page) is w = 10 ft.

A 1500-ft long horizontal and non-fractured well with 6-in. radius is completed in a 55-acre drainage area. The formation net pay is 75 ft thick with the net to gross ratio of 0.9 and has a porosity of 6.5%. The formation permeability values are 2 md and 15 md in vertical and horizontal directions, respectively with the relative permeability to oil of 0.82. The oil has a viscosity of 0.55 cp and the formation volume factor is 1.22 bbl/STB. Earlier test conducted at this well resulted in the calculation of a skin value of 0.8. The correction factor for wellbore friction is 1.0. ● Determine the Productivity Index (PI) for this well.