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Chapter 6: Problem 39
Calculate the dynamic pressure that corresponds to a speed of $100 \mathrm{km} / \mathrm{hr}$ in standard air. Express your answer in millimeters of water.
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Water flows steadily up the vertical 1-in.-diameter pipe and out the nozzle, which is 0.5 in. in diameter, discharging to atmospheric pressure. The stream velocity at the nozzle exit must be \(30 \mathrm{ft} / \mathrm{s}\). Calculate the minimum gage pressure required at section (1). If the device were inverted, what would be the required minimum pressure at section (1) to maintain the nozzle exit velocity at \(30 \mathrm{ft} / \mathrm{s} ?\)
Consider the flow field with velocity given by \(\vec{V}=\left[A\left(y^{2}-x^{2}\right)-B x | \hat{i}+[2 A x y+B y] \hat{j}, A=1 \mathrm{ft}^{-1} \cdot \mathrm{s}^{-1}, B=1\right.\) \(\mathrm{ft}^{-1} \cdot \mathrm{s}^{-1} ;\) the coordinates are measured in feet. The density is \(2 \operatorname{slug} / \mathrm{ft}^{3},\) and gravity acts in the negative \(y\) direction. Calculate the acceleration of a fluid particle and the pressure gradient at point \((x, y)=(1,1)\)
Consider the flow field with velocity given by \(\vec{V}=\) \(A x \sin (2 \pi \omega t) \hat{i}-A y \sin (2 \pi \omega t) \hat{j},\) where \(A=2 \mathrm{s}^{-1}\) and \(\omega=1 \mathrm{s}^{-1}\) The fluid density is \(2 \mathrm{kg} / \mathrm{m}^{3}\). Find expressions for the local acceleration, the convective acceleration, and the total acceleration. Evaluate these at point (1,1) at \(t=0,0.5,\) and 1 seconds. Evaluate \(\nabla p\) at the same point and times.
Heavy weights can be moved with relative ease on air cushions by using a load pallet as shown. Air is supplied from the plenum through porous surface \(A B .\) It enters the gap vertically at uniform speed, \(q\). Once in the gap, all air flows in the positive \(x\) direction (there is no flow across the plane at \(x=0\) ). Assume air flow in the gap is incompressible and uniform at each cross section, with speed \(u(x),\) as shown in the enlarged view. Although the gap is narrow \((h \ll L)\) neglect frictional effects as a first approximation. Use a suitably chosen control volume to show that \(u(x)=q x / h\) in the gap. Calculate the acceleration of a fluid particle in the gap. Evaluate the pressure gradient, \(\partial p / \partial x,\) and sketch the pressure distribution within the gap. Be sure to indicate the pressure at \(x=L\)
Water flows out of a kitchen faucet of \(1.25 \mathrm{cm}\) diameter at the rate of \(0.1 \mathrm{L} / \mathrm{s}\). The bottom of the sink is \(45 \mathrm{cm}\) below the faucet outlet. Will the cross-sectional area of the fluid stream increase, decrease, or remain constant between the faucet outlet and the bottom of the sink? Explain briefly. Obtain an expression for the stream cross section as a function of distance \(y\) above the sink bottom. If a plate is held directly under the faucet, how will the force required to hold the plate in a horizontal position vary with height above the sink? Explain briefly.
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