Question

A pipe is 26.0 m long and 4.0 cm in inner diameter, with walls 1.5 mm thick.

If air at 20 °C and 10⁵ Pa absolute pressure flows through the pipe with a velocity of 10.0 m/s, then . . .

What is the pipe cross section area (m²)?

What is the volumetric flow rate of air (m³/s)?

What is the gas density (kg/m³)?

What is the mass flow rate of air (kg/s)?

What is the air molecular mass (kg/mol)?

What is the molar flow rate of air (mol/s)?

Answer 1

inner raidus of the pipe r1 = 0.04/2 = 0.02 m

cross section area (m2) = pi r^2 = 3.14* 0.02 * 0.02 = 1.256 e -3 m^2

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volumetric flow rate of air (m3/s) = AV = 0.001256 * 10

dV/dt = 0.01256 m^3/s = 1.256 L/s

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Volume = 1.25L

use ideal gas equation as PV = nRT

n = PV/RT

n = 1 * 1.25/(0.0826 * (20+273))

n = 0.051 moles

flow rate of air 1.25* 0.051/1.25 = 0.051 mol/s

Molar mass of air = 28.97 g/mol

flow rate o air = 0.051 * 28.97 = 0.014 kg/s

Flow rate of water = 0.051 * 18 = 0.0090/s

air gas density = mass/volume = 0.014 /1.25 = 11.2 kg/m^3

mass flow rate of air (kg/s) = 0.014 kg/s

air molecular mass (kg/mol = 0.014/0.051 = 0.27 kg/mol