3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 9 = 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. U Figure for Part (a) Figure for Part (b) 300 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be a aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: /2|Aptaps|/p )
3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 9 = 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. U Figure for Part (a) Figure for Part (b) 300 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be a aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: /2|Aptaps|/p )
Elements Of Electromagnetics
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![3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at
150°. The intent is to use this cylinder as a stream
velocimeter, i.e. a device to determine the velocity of a
stream by measuring the pressures at the two taps. The
fluid is incompressible with a density of p.
Figure for Part (a)
U
Figure for Part (b)
30
a) Using potential flow approximation, derive a formula
for calculating U from the measured pressure
difference at the two pressure taps. Note that for
accurate measurement, the velocimeter must be
aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p )
b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180°
+ 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then,
calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03bab573-3455-4814-8d3d-5268e6401e29%2F121a143c-d24b-470f-9426-2966ee12175a%2F392zrzv_processed.png&w=3840&q=75)
Transcribed Image Text:3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at
150°. The intent is to use this cylinder as a stream
velocimeter, i.e. a device to determine the velocity of a
stream by measuring the pressures at the two taps. The
fluid is incompressible with a density of p.
Figure for Part (a)
U
Figure for Part (b)
30
a) Using potential flow approximation, derive a formula
for calculating U from the measured pressure
difference at the two pressure taps. Note that for
accurate measurement, the velocimeter must be
aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p )
b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180°
+ 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then,
calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )
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