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
The metallic capillary of the stalagmometer described in part B is put in contact with an electric source and acquires the increasing electric potential ϕ. The water in the stalagmometer is electrically conductive.
C.1. Determine the expression of the pressure pe, determined by the electrostatic charge, inside the spherical water drop having the radius R at the end of the tube, as a function of the electric potential ϕ. Neglect the electrostatic interaction between the drop and the rest of the system.
When the increasing electrostatic potential of the tube reaches the value ϕmax for which the pressure determined by the surface tension is equal in the module of the electrostatic pressure, the water drop having the radius R breaks and its content is sprayed.
C.2. Determine the expression ϕmax of the potential of the metal tube for which the water droplet is sprayed. Express the result as a function of R, σ and physical constants. Calculate the numerical value of this potential for the water droplet having radius R=1.0×10−3m.
Assume that when spraying the water droplet separates into n=64 identical spherical droplets.
C.3. Determine the expression of pe′ - the pressure leading to the spherical shape of the droplets formed by spraying. Express the result as a function of R, σ and physical constants. Calculate the numerical value of the pressure pe′.