A mercury thermometer has a capillary tube of 0.010-in diameter. If the bulb is made of a zero-expansion material, what volume must it have if a sensitivity of 0.10 in/f ? Is desired? Assume operation near 70 ?F. If the bulb is spherical and is immersed in stationary air, estimate the time constant.
Answers
A mercury thermometer has a capillary tube of 0.010-in diameter. If the bulb is made of a zero-expansion material, what volume must it have if a sensitivity of 0.10 in/F ? is desired? Assume operation near 70 ?F. If the bulb is spherical and is immersed in stationary air, estimate the time constant.
Use the follwing data and assumptions:
- for mercury the volume expansion coeffecient = 2n 101.4 + 10 ,
- \rho =density, c=specific heat, \rho*c=0.0162 \frac{BTU}{in^{3}-F^{\circ}}
- assume thermometer glass dimensions do not change with temperature
- assume primary resistance to heat flow is the air film resistance
- air film resistance is estimated using formula for horizontal cylinder: h = 0.2\Delta T ^{0.33} \frac{BTU}{hr-ft^{2}-F^{\circ}} where \Delta T has assumed average of 100 F^{\circ}
- Volume of sphere = \frac{4}{3}\pi r^3 = \frac{\pi*D^3}{6}
- Area of sphere = 4\pi r^2=\pi D^2
Answers: V=0.0775in^3 and \tau =810 sec