All situations take place in an enclosure thermostated at 70°C with air and saturated water vapor. The pressure is constant at p0=1.0×105N m−2.
Physical constants: g=9.8m s−2, μ0=4×10−7H m−1, ε0=8.9×10−12F m−1
Water properties: Density ρ=1.0×103kg⋅m−3, Saturated vapor pressure at 70°C ps=3.1×104N⋅m−2, Surface tension coefficient at 70°C σ=6.5×10−2N⋅m−1, Magnetic susceptibility χ=−9.0×10−6
A stalagmometer is a device used for investigating the surface tension of liquids. The device is a glass tube whose middle section is widened. The lower end of the tube is narrowed and continues with a metallic capillary tube (like a needle), to force the fluid to fall out of the tube as a droplet. The fluid flows slowly from the tube in a vertical direction. Denote with R the radius of the drop hanging below the nozzle, which grows slowly in time until the drop separates from the nozzle due to gravitation. When the droplet separates from the tube, the liquid surface forms in the vicinity of the nozzle a "neck", which has vertical tangent.
There is water in a vertically positioned stalagmometer. The metal capillary has an inside diameter d=1.0×10−4m and negligible wall thickness. The level difference between the upper surface of the water in the stalagmometer and the lower end of the capillary is constant and equal to H=5.0×10−2m. In the calculations, use the value of the surface tension that you obtained in the previous part of the problem. If you did not solve the previous part, use the value indicated in the data table.
B.1. Determine the expression of radius R of the spherical droplet that detaches from the end of the capillary tube, neglecting the contribution due to the hydrostatic pressure of the water in the stalagmometer tube. Calculate the value of radius R.
B.2. Determine the expression of radius RH of the spherical drop that detaches from the end of the capillary tube, considering the contribution due to the hydrostatic pressure of the water in the stalagmometer. Calculate the value of radius RH.