ASSIGNMENT

Assignment



Assignment

Question 1:

An Archimedes number  (not to be confused with Archimedes' constant, p), named after the ancient Greek scientist Archimedes—used to determine the motion of fluids due to density differences—is a dimensionless number in the form:

where:

g = gravitational acceleration (9.81 m/s²),

?l = density of the fluid, 

? = density of the body, 

 = dynamic viscosity, 

L = characteristic length of body, m

When analyzing potentially mixed convection of a liquid, the Archimedes number parametrizes the relative strength of free and forced convection by representing the ratio of Grashof number and the square of Reynolds number. This represents the ratio of buoyancy and inertial forces, which stands in for the contribution of natural convection. When Ar >> 1, natural convection dominates and when Ar << 1, forced convection dominates.

 

Question 2:

Velocity (ft./s)

Nusselt Number

Reynolds Number

Pressure Drop (psi/100 ft.)

Heat Transfer Coefficient (btu/h.ft2.F)

14

713.372

18876

7.66

143.82

Question 3:

Tube Layout:    

Extended Surface Type:   

Tube Id, in:

Tube Od, in:

No. Of Tube Rows:

Tubes Wide:

Tube Length, ft:

Transverse Pitch, in:

Longitudinal Pitch, in:

Fin Density, fins/in:

Fin Height/Stud Lgth, in:

Fin Thickness/Stud Dia, in:

Studs Per Plane:

Planes Per Foot:

Tube Side Process Data

Inlet Fluid Temp, F:

Outlet Fluid Temp, F:

Duty, Btu/hr:

Tube Conductivity, Btu/hr-ft:

Fluid Inside hi, Btu/hr-ft2-F:

Inside Fouling, hr-ft2-F/Btu:

Gas Side Process Data

Inlet Gas Temp, F:

Outlet Gas Temp, F:

Gas Flow, lb/hr:

Outside Fouling, hr-ft2-F/Btu:

Ext'd Surf. Cond., Btu/hr-ft:

Gas Viscosity, Cp:

Gas Therm Cond, Btu/hr-ft-F:

Gas Specific Heat, Btu/lb-F:

Gas CO2, mole %:

Gas H2O, mole %:

Question 4:

Boundary layers appear on the surface of bodies in viscous flow because the fluid seems to "stick" to the surface (*see note). Right at the surface the flow has zero relative speed and this fluid transfer's momentum to adjacent layers through the action of viscosity. Thus a thin layer of fluid with lower velocity than the outer flow develops. The requirement that the flow at the surface has no relative motion is the "no slip condition." The velocity in the boundary layer slowly increases until it reaches the outer flow velocity, Ue. 

The boundary layer thickness, d, is defined as the distance required for the flow to nearly reach Ue. We might take an arbitrary number (say 99%) to define what we mean by "nearly", but certain other definitions are used most frequently (Young & Munson, 2010: 95).

The boundary layer concept is attributed primarily to Ludwig Prandtl (1874-1953), a professor at the University of Gottingen. His 1904 paper on the subject formed the basis for future work on skin friction, heat transfer, and separation. He subsequently made fundamental contributions to finite wing theory and compressibility effects. (His name appears about 30 times in these notes.) Theodore von Karman and Max Munk were among his many famous students. R.T. Jones was a student of Max Munk and I have subsequently learned a great deal from R.T. Jones -- which makes readers of these notes great-great grandstudents of Prandtl.

The character of the boundary layer changes as it develops along the surface of the airfoil. Generally starting out as a laminar flow, the boundary layer thickens, undergoes transition to turbulent flow, and then continues to develop along the surface of the body, possibly separating from the surface under certain conditions.

In laminar flow, the fluid moves in smooth layers or lamina. There is relatively little mixing and consequently the velocity gradients are small and shear ...