Atmospheric Pressure Test Questions
Chapter 3 Pressure Measurement Examples Example 3.3 A special high pressure U tube manometer is constructed to measure pressure differential in air at 13.8 MPa and 20oC. When an oil having a specific gravity of 0.83 is used as the fluid, calculate the differential pressure in N/m2 that would be indicated by a 135 mm reading. p − pa = m g h( gc
m
−
f
)
= (0.83)(1000) = 830kg/m 3 = =
p 13.8 × 10 6 = f a RT (287)(293) g h( m − f ) p − pa = gc
= 9.81(0.135)(830 − 164.11) = 881.51N/m 2
Example 3.4 A Bridgman gauge uses a coil of Manganin wire having a nominal resistance of 100 at atmospheric pressure. The gauge is to be used to measure a pressure of 1 MPa with an uncertainty of 0.1 percent. What is the allowable uncertainty in the resistance measurement? The pressure coefficient of resistance of Manganin is 2.5 x 10-11Pa-1.
R = R1 (1 + b∆p ) ∂R = R1b = 100 2.5 × 10 −11 = 2.5 × 10 −9 ∂∆p
∆p
(
)
= 1MPa × 0.1% = 1000 ∂R ∂∆p
2 ∆p 1 2
R
=
= ___________
Example 3.5 A Bridgman gauge is to be used to measure a pressure of 20 MPa using a Manganin element having a resistance of 100 at atmospheric pressure. Calculate the resistance of the gauge under high pressure conditions. If the gauge is one leg of a Wheatstone bridge whose other legs all have values of exactly 100 , calculate the voltage output for a constant-voltage source of 24 V.
R = R1 (1 + b∆p )
= 100 1 + 2.5 × 10 −11 × 20 × 10 6 = 100.05Ω
(
)
At E=24 V, R4=100.05 , R1=R2=R3=100
Eg = E R1 R2 − R1 + R4 R2 + R3
= ____________ V
Example 3.6 A McLeod gauge has a capillary diameter of 0.2 mm and a volume Vb of 125 mm3. What gauge reading will result from an absolute pressure of 20 µm? VB=1.25 ×105 mm3 ; VC= ay = (0.2) 2y/4 p= 20 µm ay 2 = 0.02mm VB y = 282 mm
m
−
f
)
= (0.83)(1000) = 830kg/m 3 = =
p 13.8 × 10 6 = f a RT (287)(293) g h( m − f ) p − pa = gc
= 9.81(0.135)(830 − 164.11) = 881.51N/m 2
Example 3.4 A Bridgman gauge uses a coil of Manganin wire having a nominal resistance of 100 at atmospheric pressure. The gauge is to be used to measure a pressure of 1 MPa with an uncertainty of 0.1 percent. What is the allowable uncertainty in the resistance measurement? The pressure coefficient of resistance of Manganin is 2.5 x 10-11Pa-1.
R = R1 (1 + b∆p ) ∂R = R1b = 100 2.5 × 10 −11 = 2.5 × 10 −9 ∂∆p
∆p
(
)
= 1MPa × 0.1% = 1000 ∂R ∂∆p
2 ∆p 1 2
R
=
= ___________
Example 3.5 A Bridgman gauge is to be used to measure a pressure of 20 MPa using a Manganin element having a resistance of 100 at atmospheric pressure. Calculate the resistance of the gauge under high pressure conditions. If the gauge is one leg of a Wheatstone bridge whose other legs all have values of exactly 100 , calculate the voltage output for a constant-voltage source of 24 V.
R = R1 (1 + b∆p )
= 100 1 + 2.5 × 10 −11 × 20 × 10 6 = 100.05Ω
(
)
At E=24 V, R4=100.05 , R1=R2=R3=100
Eg = E R1 R2 − R1 + R4 R2 + R3
= ____________ V
Example 3.6 A McLeod gauge has a capillary diameter of 0.2 mm and a volume Vb of 125 mm3. What gauge reading will result from an absolute pressure of 20 µm? VB=1.25 ×105 mm3 ; VC= ay = (0.2) 2y/4 p= 20 µm ay 2 = 0.02mm VB y = 282 mm