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Chapter 8: Problem 10

How is the hydrodynamic entry length defined for flow in a tube? Is the entry length longer in laminar or turbulent flow?

Short Answer

Expert verified
Answer: Hydrodynamic entry length is the distance from the inlet of a tube or a pipe, where the flow develops from a non-uniform velocity profile to a fully developed one. This is the distance required for the fluid flowing through a tube to adjust to being confined within the pipe and exhibit a stable velocity profile. The entry length is longer in turbulent flow than in laminar flow due to the chaotic motion of fluid particles and the need for a longer distance to achieve a fully developed flow profile.

Step by step solution

01

Define hydrodynamic entry length

The hydrodynamic entry length is the distance from the inlet of a tube or a pipe, where the flow develops from a non-uniform velocity profile to a fully developed one. In other words, it is the distance required for the fluid flowing through a tube to adjust to being confined within the pipe and exhibit a stable velocity profile.
02

Laminar flow entry length

In laminar flow (when the Reynolds number is less than 2100), the fluid particles move in parallel layers with no disruption between them. The entry length for laminar flow in a tube can be calculated using the following formula: Entry Length (L) = 0.05 * (Re) * D where Re is the Reynolds number (dimensionless) and D is the diameter of the tube.
03

Turbulent flow entry length

In turbulent flow (when the Reynolds number is greater than 4000), the fluid particles move in random and chaotic motion with eddies and swirls. The entry length for turbulent flow in a tube can be calculated using the following formula: Entry Length (L) = 4.4 * (Re ^ (1/6)) * D where Re is the Reynolds number (dimensionless) and D is the diameter of the tube.
04

Comparison of entry lengths in laminar and turbulent flows

Comparing the formulas for entry lengths in laminar and turbulent flows, we can see that the entry length for turbulent flow is generally larger than that for laminar flow due to the chaotic motion of fluid particles and the need for a longer distance to achieve a fully developed flow profile. So, the entry length is longer in turbulent flow than in laminar flow.

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Most popular questions from this chapter

Air \(\left(c_{p}=1007 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) enters a 17 -cm-diameter and 4-m-long tube at \(65^{\circ} \mathrm{C}\) at a rate of \(0.08 \mathrm{~kg} / \mathrm{s}\) and leaves at \(15^{\circ} \mathrm{C}\). The tube is observed to be nearly isothermal at \(5^{\circ} \mathrm{C}\). The average convection heat transfer coefficient is (a) \(24.5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (b) \(46.2 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (c) \(53.9 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (d) \(67.6 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (e) \(90.7 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)

Water enters a circular tube whose walls are maintained at constant temperature at a specified flow rate and temperature. For fully developed turbulent flow, the Nusselt number can be determined from \(\mathrm{Nu}=0.023 \mathrm{Re}^{0.8} \mathrm{Pr}^{0.4}\). The correct temperature difference to use in Newton s law of cooling in this case is (a) The difference between the inlet and outlet water bulk temperature. (b) The difference between the inlet water bulk temperature and the tube wall temperature. (c) The log mean temperature difference. (d) The difference between the average water bulk temperature and the tube temperature. (e) None of the above.

Consider the flow of oil at \(10^{\circ} \mathrm{C}\) in a 40 -cm-diameter pipeline at an average velocity of \(0.5 \mathrm{~m} / \mathrm{s}\). A \(1500-\mathrm{m}\)-long section of the pipeline passes through icy waters of a lake at \(0^{\circ} \mathrm{C}\). Measurements indicate that the surface temperature of the pipe is very nearly \(0^{\circ} \mathrm{C}\). Disregarding the thermal resistance of the pipe material, determine \((a)\) the temperature of the oil when the pipe leaves the lake, \((b)\) the rate of heat transfer from the oil, and \((c)\) the pumping power required to overcome the pressure losses and to maintain the flow of oil in the pipe.

Air ( \(1 \mathrm{~atm})\) enters into a 5 -cm-diameter circular tube at \(20^{\circ} \mathrm{C}\) with an average velocity of \(5 \mathrm{~m} / \mathrm{s}\). The tube wall is maintained at a constant surface temperature of \(160^{\circ} \mathrm{C}\), and the outlet mean temperature is \(80^{\circ} \mathrm{C}\). Estimate the length of the tube.

Engine oil flows in a \(15-\mathrm{cm}\)-diameter horizontal tube with a velocity of \(1.3 \mathrm{~m} / \mathrm{s}\), experiencing a pressure drop of \(12 \mathrm{kPa}\). The pumping power requirement to overcome this pressure drop is (a) \(190 \mathrm{~W}\) (b) \(276 \mathrm{~W}\) (c) \(407 \mathrm{~W}\) (d) \(655 \mathrm{~W}\) (e) \(900 \mathrm{~W}\)
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