contestada

A certain rigid aluminum container contains a liquid at a gauge pressure of P0 = 2.02 × 105 Pa at sea level where the atmospheric pressure is Pa = 1.01 × 105 Pa. The volume of the container is V0 = 4.4 × 10-4 m3. The maximum difference between the pressure inside and outside that this particular container can withstand before bursting or imploding is ΔPmax = 2.26 × 105 Pa. For this problem, assume that the density of air maintains a constant value of rhoa = 1.20 kg / m3 and that the density of seawater maintains a constant value of rhos = 1025 kg / m3.What is the maximum height h in meters above the ground that the container can be lifted before bursting?

Respuesta :

Answer:

[tex]dz=19217687.07\ m[/tex]

Explanation:

Given:

  • initial gauge pressure in the container, [tex]P_0=2.02\times 10^{5}\ Pa[/tex]
  • atmospheric pressure at sea level, [tex]P_a=1.01\times 10^5\ Pa[/tex]
  • initial volume, [tex]V_0=4.4\times 10^{-4}\ m^3[/tex]
  • maximum pressure difference bearable by the container, [tex]dP_{max}=2.26\times 10^{5}\ Pa[/tex]
  • density of the air, [tex]\rho_a=1.2\ kg.m^{-3}[/tex]
  • density of sea water, [tex]\rho_s=1.2\ kg.m^{-3}[/tex]

The relation between the change in pressure with height is given as:

[tex]\frac{dP_{max}}{dz} =\rho_a.g_n[/tex]

where:

dz = height in the atmosphere

[tex]g_n[/tex]= standard value of gravity

Now putting the respective values:

[tex]\frac{2.26\times 10^{5}}{dz} =1.2\times 9.8[/tex]

[tex]dz=19217.687\ km[/tex]

[tex]dz=19217687.07\ m[/tex]

Is the maximum height above the ground that the container can be lifted before bursting. (Since the density of air and the density of sea water are assumed to be constant.)

Otras preguntas