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Chapter 8: Problem 19
A fluid flows through a horizontal 0.1-in.-diameter pipe. When the Reynolds number is \(1500,\) the head loss over a \(20-f t\) lenzth of the pipe is \(6.4 \mathrm{ft}\). Determine the fluid velocity.
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The Churchill formula for the friction factor is $$f=8\left[\left(\frac{8}{\mathrm{Re}}\right)^{12}+\frac{1}{(A+B)^{15}}\right]^{1 / 12}$$ where $$\begin{array}{l} A=\left\\{-2.457 \ln \left[\left(\frac{7}{\mathrm{Re}}\right)^{0.9}+\frac{\varepsilon}{3.7 D}\right]\right\\}^{16} \\ B=\left(\frac{37.530}{\mathrm{Re}}\right)^{16} \end{array}$$ Compare this equation for \(f\) for both the laminar and turbulent regimes for \(\varepsilon / D=0.00001,0.0001,0.001,\) and 0.01 and Reynolds numbers of \(10,10^{2}, 10^{3}, 10^{4}, 10^{5}, 10^{6},\) and \(10^{7}\) with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.
{ Blood iassume } \mu=4.5 \times 10^{-5} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}, S G=1.0\right)\( flows through an artery in the neck of a giraffe from its heart to its head at a rate of \)2.5 \times 10^{-4} \mathrm{ft}^{3} / \mathrm{s}\(. Assume the length is \)10 \mathrm{ft}\( and the diameter is 0.20 in. If the pressure at the beginning of the artery (outlet of the heart) is equivalent to \)0.70 \mathrm{ft}$ Hg, determine the pressure at the end of the artery when the head is (a) 8 ft above the heart, or (b) 6 ft below the heart. Assume steady flow. How much of this pressure difference is due to elevation effects, and how much is due to frictional effects?
A viscous fluid flows in a 0.10 -m-diameter pipe such that its velocity measured \(0.012 \mathrm{m}\) away from the pipe wall is \(0.8 \mathrm{m} / \mathrm{s}\) If the flow is laminar, determine the centerline velocity and the flowrate.
When soup is stirred in a bowl, there is considerable turbulence in the resulting motion (see Video \(\mathrm{V} 8.7\) ). From a very simplistic standpoint, this turbulerce consists of numerous intertwined swirls, each involving a characteristic diameter and velocity. As time goes by, the smaller swirls (the fine scale structure) die out relatively quickly, leaving the large swirls that continue for quite some time. Explain why this is to be expected.
The wall shear stress in a fully developed flow portion of a 12-in.-diameler pipe carrying water is 1.85 Ib/ft? Determine the pressure gracient, \(\partial p / \partial x,\) where \(x\) is in the flow direction, if the pipe is (a) horizontal, (b) vertical with flow up, or (c) vertical with flow down.
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