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Chapter 8: Problem 40

Carbon dioxide at a temperature of \(0^{\circ} \mathrm{C}\) and a pressure of \(600 \mathrm{kPa}(\text { abs })\) flows through a horizontal \(40-\mathrm{mm}\) -diameter pipe with an average velocity of \(2 \mathrm{m} / \mathrm{s}\). Determine the friction factor if the pressure drop is \(235 \mathrm{N} / \mathrm{m}^{2}\) per 10 -m length of p pe.

Short Answer

Expert verified
By methodically applying the theories and formulas of fluid dynamics and fluid flow, the friction factor for the given problem can be calculated. Exact figures depend on the provided input values such as viscosity and density specific to the fluid and temperature.

Step by step solution

01

Calculation of Reynolds Number

Firstly, the Reynolds number (Re) needs to be calculated since it is imperative in determining the flow regime and friction factor. The formula for Reynolds number is given by: \( Re = \frac{dV\rho}{\mu} \) Where: d = Diameter of the pipe, V = Velocity, \(\rho\) = Density (which can be found using the given temperature and pressure), \(\mu\) = Dynamic viscosity (which can also be found using the given temperature)
02

Determination of Flow Regime

Using the value of the Reynolds number obtained from the previous step, the type of flow stream should be determined. The criteria are as follows: for \( Re < 2000 \), the flow is laminar; for \( 2000 ≤ Re ≤ 4000 \), the flow is transitional; and for \( Re > 4000 \), the flow is turbulent. Once the flow regime is determined, it is easily possible to navigate towards the right friction factor equation.
03

Calculation of friction factor

The friction is calculated differently based on the flow regime. For laminar flow: The friction factor \( f = \frac{64}{Re} \). For turbulent flow, a suitable approximation is the Haaland equation: \( f = \frac{1}{[1.8log_{10}(\frac{6.9}{Re} + (\frac{\varepsilon}/{3.7d})^{1.11})]^2} \). Here \(\varepsilon\) represents the absolute roughness of the pipe (if not given, a pipe's roughness can usually be found in engineering tables).
04

Validation of Calculated Friction Factor

After calculating the friction factor, the value can be validated by applying the Darcy's formula: \( \Delta p = f (\frac{L}{D}) (\frac{\rho V^2}{2}) \). Here, \( \Delta p \) is the pressure drop, L is the length of the pipe, and D is the diameter of the pipe. If the calculated pressure drop matches the given one, the calculated friction factor has been validated.

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Most popular questions from this chapter

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