A pipe, of cross-sectional area 0.1 m^2, carries a flow of 75 % O2 and 25 % N2 by mole with a ve

A pipe, of cross-sectional area 0.1 m^2, carries a flow of...

A pipe, of cross-sectional area $0.1 \mathrm{m}^{2},$ carries a flow of $75 \% \mathrm{O}_{2}$ and $25 \% \mathrm{N}_{2}$ by mole with a velocity of $25 \mathrm{m} / \mathrm{s}$ at $200 \mathrm{kPa}$ and $290 \mathrm{K} .$ To install and operate a mass flow meter, it is necessary to know the mixture density and the gas constant. What are they? What mass flow rate should the meter then show?

Key Concepts

Mass Flow Rate

The mass flow rate is calculated as the product of the density of the fluid, the cross-sectional area through which the fluid flows, and the velocity of the flow (? = ?·A·v). This parameter is key in evaluating the performance of fluid systems and is particularly important when installing and calibrating flow measurement devices like mass flow meters.

Ideal Gas Law

The ideal gas law (PV = nRT) provides a fundamental relationship among pressure, volume, temperature, and amount of gas, and when rearranged with density (? = mass/volume) and the specific gas constant (R_specific), it allows for the calculation of a gas’s density (? = P/(R_specific·T)). This relationship is central to understanding and computing the properties of gases under various conditions.

Gas Mixture Composition

Gas mixtures are handled by considering the mole fractions or mass fractions of the individual components. The properties of the mixture, such as the average molar mass or specific gas constant, are computed as weighted averages based on these fractions, ensuring that the thermodynamic behavior accurately reflects the contributions of each gas.

Specific Gas Constant

The specific gas constant for any gas is defined as R_specific = R_universal/M, where R_universal is the universal gas constant and M is the molar mass. For gas mixtures, an effective molar mass is obtained by summing the products of each component's molar mass and its mole fraction. This constant is essential for applying the ideal gas law to mixtures.

Density Calculation for Gases

Using the ideal gas law rearranged for density, one obtains ? = P/(R_specific·T). This formula is used to calculate the density of a gas or gas mixture by knowing the pressure, temperature, and specific gas constant, linking microscopic properties with measurable quantities.

Transcript

00:01 Hi, everybody.

00:02 So for this one is, is it necessary to know the mixture of density and the gas constant? and what are they? and what mass flow weight should a meter even still? the answer is yes, okay? it is important.

00:18 And what we can do is find the m mix, okay? and that is just going to be the m -i -thing -j -i.

00:30 And here we have 0 .75.

00:33 Times 31 .999 plus 0 .25 times 28 .013.

00:46 And the reason i know that is because this is 75%, and this is the 25 % for the 02 and this is for the n2.

01:01 Okay? and that's how i know that.

01:04 And i can find the y simply by just looking at book.

01:10 Okay.

01:11 And so your m -m -m -m -m -mix is going to be 31 .00 -2 -5.

01:17 And now to find our mix is what i was looking for.

01:21 We have the r -rate in the mix down here.

01:26 So we have 8 .314, and that's just a constant, and that's the blue line about.

01:31 Here represent and we have 31 .0025 and this is going to be 0 .26817 kilon tools for kilogram times kelvin okay and now it was asking about finding mass flow rate and meter in the shell so we can simply just do the flow rate as actually, we need to find the volume first.

02:06 So we'll find them volume.

02:08 So we have p and actually the whole, this is a short cut way.

02:11 So we have the volume that's going to be r mix times t divided by a pressure...

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