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Chapter 8 Solutions
Loose Leaf for Fundamentals of Aerodynamics
- 4. Consider a wide liquid film of constant thickness h flowing steadily due to gravity down an inclined plane at angle 0. AS shown in below figure. The atmosphere exerts constant pressure and negligible shear on the free surface. Show that the velocity distribution is given by pg sine u y(2h-y) 2µ and that the volume flow rate per unit width is Q pgh3 sin 0 /3µ. u(y)arrow_forwardYour team is designing a chemical processing plant. You are the liquid handling and transportation specialist, and you need to transport a solvent (μ = 3.1 cP, ρ = 122k kg/m3) from a storage tank to a reaction vessel. Due to other equipment constraints, the fluid velocity must be 0.8 m/sec, and you must use stainless steel piping (ε = 0.00015 mm) with a total length (L) of 12 m. Determine the pipe inner diameter (ID) you will need to achieve a pressure drop of 0.3 kPa. Use the Moody chart.arrow_forwardAt a given point in a flow, T = 700 ◦R, p = 1.6 atm, and V = 2983 ft/s.At this point, calculate the corresponding values of p0, T0, p∗, T ∗, and M∗.arrow_forward
- A constant-thickness film of viscous liquid (SG = 0.8, μ = 0.5 Pa-s) flows down an inclined plate an angle of 10⁰ as shown in the figure The velocity profile is given by the equation, u(y) = Cy(2h — y). If the value of his 5 cm, what is the value of the maximum velocity in m/s? NOTE: The pressure does not vary along the flow direction. u(y) Answer:arrow_forwardIn a tapered horizontal pipeline, the seawater's speed is 3.75 m/s and the gauge pressure is 21 kPa at the first point. Find the gauge pressure at a second point in the line if the cross-sectional area at the second point is thrice that at the first.arrow_forward1 Consider a rapidly rotating (ie, in near geostrophic balance) Boussineq fluid on the f plane. A) Show that the pressure divided by the density scales as Φ ≈ fUL B) Show that the horizontal divergence of the geostrophic wind vanishes. Thus, argue that the scaling W ≈ UH = L is an overestimate for the magnitude of the vertical velocityarrow_forward
- the velocity principle of a given fluid flowing over a flat plate is given by = 2y – y 2 , where u in inches and y in inches .find shear stress at y = 0 and 1 ,respectively , if the fluid viscosity is 0.006 lbf s/ft 2 .arrow_forwardA fire hose has an inside diameter of 6.5 cm. Suppose such a hose carries a water flow of 40.5 L/s starting at a gauge pressure of 1.68 × 106 N/m2 . The hose discharges through a nozzle having an inside diameter of 3.4 cm. Take the viscosity of water to be 1.005 × 10-3 (N/m2)⋅s dh = 6.5 cmdn = 3.4 cmP = 1.68 × 106 N/m2Q = 40.5 L/s a. the Reynolds number, NR, for flow in the fire hose to show that the flow must be turbulent, with NR≥ 3000. b. Calculate the Reynolds number, NR, for flow in the fire hose and nozzle to show that the flow must be turbulent, with NR≥ 3000.arrow_forwardQ2. The laminar flow of a Newtonian fluid between parallel plates is illustrated in the below figure. The velocity distribution for this flow is : h2 aP V = 8µ ax h The total gap between the plates is 3 cm. The viscosity of the fluid is 0.5 N s/m and the pressure gradient is -1200 N/m?/m. Find the magnitude and direction of the shear stress on the upper plate.arrow_forward
- The figure shows a channel with width of 2.4 m. The density of the water is 1000 kg/m^3. The flow is steady. At the entrance of the channel, the flow is uniform with velocity V (m/s) while at the exit, the flow has developed the shown velocity profile u(y) = 4y-2y^2 (m/s) and y is in (m). Answer the following questions. A)The mass flow rate in (kg/s) at the entrance ? b)The velocity in (m/s) at the inlet ?arrow_forwardA viscous fluid of viscosity 2.48 Pa-s and density 884 kg/m³ is dragged by a rigid flat surface that moves upward with speed V, as shown. The velocity profile in the fluid layer is of the form, pg v(x) = (x? – 2hx) + V Find the minimum speed V for which the entire fluid layer moves upward. What are the minimum and maximum values of the shear stress in the layer? Assume the flow to be incompressible and fully developed. 5 mmarrow_forwardQ: Consider fully developed laminar flow in the annular space formed by the two concentric cylinders shown in the below diagram. The outer pipe is stationary, and the inner pipe moves in the x direction with speed V For pressure gradient, , and the inner cylinder stationary, let ro = R and r = kR, The velocity profile is ax given by: др + 4μ. θα Find: 1- Volume flow rate (Q). 2- An expression for the average velocity (V) 3- Fork → 0, find Q and V 6arrow_forward
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