Answer to Question #269101 in Classical Mechanics for joseph

Question

1. The variation of pressure P in gas with density p is given by P = Cpⁿ where C and n and are constants with P = P_o and p = p₀, at elevation z = 0. Obtain a relation for the variation of P with elevation in terms of z. g. n. P_o and p_o.

2. A manometer containing oil (p₀ = 850 kg/m³) is attached to a tank filled with air. If the oil-level difference between the two columns is I50 cm and the atmospheric pressure is 98 kPa, determine the absolute pressure of the air in the tank. 

Answer 1

1.

$P=C\rho^n,$

$P=P_0e^{-\frac{mgh}{RT}},$

$n=1,$

$\rho=\frac{PM}{RT},$

$C=\frac{RT}M,$

$P=P_0e^{-\frac{mgh \rho_0}{P_0M}}.$

2.

$P=P_0+\rho gh=110.5~kPa.$