Chapter 2: Problem 80
Slowly fill a glass with water to the maximum possible level. Observe the water level closely. Explain how it can be higher than the rim of the glass.
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Chapter 2: Problem 80
Slowly fill a glass with water to the maximum possible level. Observe the water level closely. Explain how it can be higher than the rim of the glass.
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Plan an experiment to measure the surface tension of a liquid similar to water. If necessary, review the NCFMF video Surface Tension for ideas. Which method would be most suitable for use in an undergraduate laboratory? What experimental precision could be expected?
Consider the garden hose of Fig. \(2.5 .\) Suppose the velocity field is given by \(\vec{V}=u_{0} \hat{i}+v_{0} \sin \left[\omega\left(t-x / u_{0}\right)\right] \hat{j},\) where the \(x\) direction is horizontal and the origin is at the mean position of the hose, \(u_{0}=10 \mathrm{m} / \mathrm{s}, v_{0}=2 \mathrm{m} / \mathrm{s},\) and \(\omega=5\) cycle/s. Find and plot on one graph the instantancous streamlines that pass through the origin at \(t=0\) s, 0.05 s, 0.1 s, and 0.15 s. Also find and plot on one graph the pathlines of particles that left the origin at the same four times.
Tape is to be coated on both sides with glue by drawing it through a narrow gap. The tape is 0.015 in. thick and 1.00 in. wide. It is centered in the gap with a clearance of 0.012 in. on each side. The glue, of viscosity \(\mu=0.02\) slug \(/(\mathrm{ft} \cdot \mathrm{s})\) completely fills the space between the tape and gap. If the tape can withstand a maximum tensile force of 25 lbf, determine the maximum gap region through which it can be pulled at a speed of 3 ft/s.
For the velocity fields given below, determine: a. whether the flow field is one- , two-, or three-dimensional, and why. b. whether the flow is steady or unsteady, and why. (The quantities \(a\) and \(b\) are constants.) (1) \(\vec{V}=\left[a y^{2} e^{-b t}\right]\) (2) \(\vec{V}=a x^{2} i+b x j+c k\) (3) \(\vec{V}=\)axyi\(-\)byt (4) \(\vec{V}=a x \hat{i}-b y j+c t \hat{k}\) (5) \(\bar{V}=\left[a e^{-\ln x}\right] i+b t^{2}\) (6) \(\vec{V}=a\left(x^{2}+y^{2}\right)^{1 / 2}\left(1 / z^{3}\right) \hat{k}\) (7) \(\vec{V}=(a x+t) i-b y^{2}\) (8) \(\vec{V}=a x^{2} \hat{i}+b x z j+c y k\)
The velocity distribution for laminar flow between parallel plates is given by \\[\frac{u}{u_{\max }}=1-\left(\frac{2 y}{h}\right)^{2}\\] where \(h\) is the distance separating the plates and the origin is placed midway between the plates. Consider a flow of water at \(15^{\circ} \mathrm{C},\) with \(u_{\max }=0.10 \mathrm{m} / \mathrm{s}\) and \(h=0.1 \mathrm{mm} .\) Calculate the shear stress on the upper plate and give its direction. Sketch the variation of shear stress across the channel.
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