Manometer problem
The velocity of a flow can be found by measuring the total pressure (
ܲ
௧
) measured at the forward
stagnation point, and the static pressure (
ܲ
௦
) in a region where the flow is parallel to the free
‐
stream
over a significant distance. A device for making this measurement is a Pitot tube. The velocity is then
given by the equation
ܲ
௧
െܲ
௦
ൌ
ଵ
ଶ
ߩܸ
ଶ
. A water manometer is connected both the total and static lines
from a pitot tube and the difference in height between the legs of the manometer was measured to be
30 cm. What is the pressure difference between the total and static pressures? What is the speed of
the flow? What is the Mach number? The air temperature is 298K. What is the Reynolds number for a
wing model with a 20cm chord?
Table from the inside cover of Munson, Young and Okiishi, “Fundamentals of Fluid Mechanics,” 3
rd
ed.
New York (Wiley & Sons) 1990.
∆ܲ ൌ ߩ݃∆݄ ൌ ሺ1000݇݃/݉
ଷ
ሻሺ9.81݉/ݏ
ଶ
ሻሺ0.300݉ሻ ൌ 2940ܰ/݉
ଶ
ܸൌ ඥ2∆ܲ/ߩ
ൌ ඥ2ሺ2940ܰ/݉
ଶ
ሻ/ሺ1.23݇݃/݉
ଷ
ሻ
ൌ69
.1݉/ݏ
ܽൌ ඥߛܴܶ
ൌ ඥሺ1.4ሻሺ287 ܬ/݇݃ܭሻሺ298ܭሻ
ൌ 346݉/ݏ
ܯൌ
ܸ
ܽ
ൌ
69.1݉/ݏ
346݉/ݏ
ൌ 0.200
ܴ݁ ൌ
ߩܸܿ
ߤ
ൌ
ሺ1.23݇݃/݉
ଷ
ሻሺ69.1݉/ݏሻሺ0.20݉ሻ
1.79 ൈ 10
ିହ
ܰݏ/݉
ଶ
ൌ 950,000
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentReview of vectors and vector operations
ଙ̂
,
ଚ̂
,
are unit vectors in the x, y and z directions
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 Munday
 lim, Hebrew numerals, Airline hub

Click to edit the document details