Download Cost-effectiveness: An Engineers`s Real Job

Cost-effectiveness: An
Engineers's Real Job
Problem 3.138*
Created By: Patrick Thomas
Problem
•A pitot-static probe to measure the velocity
distribution in a water tunnel at 20o C.
•U-tube manometer that uses a liquid of specific
gravity 1.7.
•Maximum velocity= Vmax= 2.3 m/s.
•U-tube manometers to choose from are 8, 12,
16, 24, and 36 inches, with increasing cost
(respectively).
Which U-tube manometer should be purchased?
Assumptions
• Incompressible flow
p  0
• One-dimensional flow
• Steady flow
Important Formulae
• The Pitot Formula:
 ( p  ps ) 
V  2 0




1
2

p0  p s 
1
V 2
2
• Hydrostatic Relationship for Manometer
p down  pup    z
• Specific gravity  Specific Weight
Spec.g 
 liquid
 1.7
 water
 liquid  1.7   water  1696.6 kg
m3
Calculations
• Using the rearranged Pitot Equation, we can solve for the pressure
difference:
p0  p s 
1
V 2  2639 Pa
2
• With the pressure difference and specific weight, we can solve for
the displaced liquid using the hydrostatic equation:
pdown  pup    z
2639 Pa  (16643.646)z
z  .1586m  6.24in
Discussion
Although an 8 inch manometer would
suffice, I suggest purchasing a 12 inch
manometer (for a factor of safety of 2).
Relation to Biofluids
• The pitot-static probe measures slow moving fluids well.
• Thus, the pitot-static probe would make a great blood pressure
measurement device.
• The pitot-static probe runs into problems when the flow is not
laminar, however.