Respuesta :
Answer:
a) The difference between the pressures at the centers of the bottom and top surfaces is 21756 N/m²
b) The difference between the pressures at the center and the edge of the bottom surface is 7156.69 N/m²
Explanation:
Given:
D = diameter of the cylinder = 1.2 m
z₂ - z₁ = height of the cylinder = 3 m
ρ = density of gasoline = 740 kg/m³
N = rotational speed = 70 rpm
The angular velocity is equal:
[tex]w=\frac{2\pi N}{60} =\frac{2\pi 70}{60} =7.33rad/s[/tex]
a) The difference pressure between two points is:
[tex]P_{2} -P_{1} =\frac{\rho w^{2} }{2} (r_{2}^{2} -r_{1}^{2} )-\rho g(z_{2} -z_{1} )[/tex]
r₂ - r₁ = 0
[tex]P_{2} -P_{1} =0-\rho g(z_{2} -z_{1} )=-740*9.8*3=-21756N/m^{2} =21756N/m^{2}[/tex]
b) The difference pressure is:
[tex]P_{2} -P_{1} =\frac{\rho w^{2}(R_{2}^{2}-0)-0 }{2} =\frac{740*7.33^{2}*0.6^{2} }{2} =7156.69N/m^{2}[/tex]
