A closed vessel of volume 80 litres contain gas at a gauge pressure of 150 kPa. If the gas is compressed isothermally to half its volume, determine the resulting pressure.

Answer:

The resulting pressure is 300 kilopascals.

Explanation:

Let consider that gas within the closed vessel behaves ideally. By the equation of state for ideal gases, we construct the following relationship for the isothermal relationship:

[tex]P_{1}\cdot V_{1} = P_{2} \cdot V_{2}[/tex] (1)

Where:

[tex]P_{1}[/tex], [tex]P_{2}[/tex] - Initial and final pressure, measured in kilopascals.

[tex]V_{1}[/tex], [tex]V_{2}[/tex] - Initial and final volume, measured in litres.

If we know that [tex]\frac{V_{1}}{V_{2}} = 2[/tex] and [tex]P_{1} = 150\,kPa[/tex], then the resulting pressure is:

[tex]P_{2} = P_{1}\times \frac{V_{1}}{V_{2}}[/tex]

[tex]P_{2} = 300\,kPa[/tex]

The resulting pressure is 300 kilopascals.

An infinite cylindrical rod falls down in the middle of an infinite tube filled with fluidat a constant speed V (terminal velocity). The density of the rod and the fluid are different.Assume that the pressure field is hydrostatic.(a)[5pts] Solve for the velocity profileas a function of rin terms of V and the other variables.(b)[2pts] Calculate upward force per unit length of the rod from the fluid wall shear stress on the rod.(c)[2 pts] Calculate upward force per unit length of the rod from bouyancy.(d)[1pts] Calculate V.VR1