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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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Consider the flow field represented by the potential function $\phi=A x^{2}+B x y-A y^{2} .$ Verify that this is an incompressible flow and determine the corresponding stream function.
Water flows at low speed through a circular tube with inside diameter of 2 in. A smoothly contoured body of 1.5 in. diameter is held in the end of the tube where the water discharges to atmosphere. Neglect frictional effects and assume uniform velocity profiles at each section. Determine the pressure measured by the gage and the force required to hold the body.
Water flows in a circular duct. At one section the diameter is \(0.3 \mathrm{m}\), the static pressure is \(260 \mathrm{kPa}\) (gage), the velocity is \(3 \mathrm{m} / \mathrm{s},\) and the elevation is \(10 \mathrm{m}\) above ground level. At a section downstream at ground level, the duct diameter is \(0.15 \mathrm{m}\) Find the gage pressure at the downstream section if frictional effects may be neglected.
In a two-dimensional frictionless, incompressible \(\left(\rho=1500 \mathrm{kg} / \mathrm{m}^{3}\right)\) flow, the velocity field in meters per second is given by \(\vec{V}=(A x+B y) \hat{i}+(B x-A y) \hat{j} ;\) the coordinates are measured in meters, and \(A=4 \mathrm{s}^{-1}\) and \(B=2 \mathrm{s}^{-1}\). The pressure is \(p_{0}=200 \mathrm{kPa}\) at point \((x, y)=(0,0) .\) Obtain an expression for the pressure field, \(p(x, y)\) in terms of \(p_{0}, A,\) and \(B,\) and evaluate at point \((x, y)=(2,2)\)
Consider frictionless, incompressible flow of air over the wing of an airplane flying at \(200 \mathrm{km} / \mathrm{hr}\). The air approaching the wing is at 65 kPa and \(-10^{\circ} \mathrm{C}\). At a certain point in the flow, the pressure is 60 kPa. Calculate the speed of the air relative to the wing at this point and the absolute air speed.
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