Consider the curved duct of Prob. 6-41, except 4Ilow the cross-sectional area to vary along the duct
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Fluid Mechanics: Fundamentals and Applications
- An oil film drains steadily down the side of a vertical wall, as shown on figure below. After an initial development at the top of the wall it attains a fully-developed draining vertical oil- film wherein the film becomes independent of "z" and of constant wall thickness. Let the vertical velocity as (w) and using the nomenclatures in the figure such as distance from plate (x), fluid properties, gravity (g) and film thickness ( ). Perform dimensional analysis and determine the function in terms of dimensionless parameters.arrow_forwardAn incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is rt of this book may be reproarrow_forwardTwo infinite plates a distance h apart are parallel to the xzplane with the upper plate moving at speed V, as inFig. There is a fluid of viscosity μ and constant pressurebetween the plates. Neglecting gravity and assumingincompressible turbulent flow u(y) between the plates, usethe logarithmic law and appropriate boundary conditions toderive a formula for dimensionless wall shear stress versusdimensionless plate velocity. Sketch a typical shape of theprofile u(y).arrow_forward
- 3-16. Consider a film of liquid draining at volume flow rate Q down the outside of a verti- cal rod of radius a, as shown in Fig. P3-16. Some distance down the rod, a fully devel- oped region is reached where fluid shear balances gravity and the film thickness remains constant. Assuming incompressible laminar flow and negligible shear inter- action with the atmosphere, find an expression for v₂(r) and a relation between Q and film radius b.arrow_forwardWater flows steadily downward along a pipe that is inclined at 30° below the horizontal, as shown. Pressure difference P4-PB is due partly to gravity and partly to friction. Evaluate the pressure difference if L = 1.5 m and h = 15 cm. Use p= 1000 kg/m3 and u = 1.12 x 103 Ns/m2 for the water and p= 13600 kg/m³ and u = 1.57 x 103 Ns/m? for the mercury. L Water 30°7 Mercury harrow_forwardTake the full-blown Couette flow as shown in the figure. While the upper plate is moving and the Lower Plate is constant, flow occurs between two infinitely parallel plates separated by the H distance. The flow is constant, uncompressed, and two-dimensional in the X-Y plane. In fluid viscosity µ, top plate velocity V, distance h, fluid density ρ, and distance y, create a dimensionless relationship for component X of fluid velocity using the method of repeating variables. Show all steps in order.arrow_forward
- A vertical U-tube partially filled with alcohol (SG= 0.99) is rotated at a specified rate about its left arm. Compute for the following: (a) angular velocity of the tube's rotation if the alcohol is on the brink of spilling (b) pressure at point B during the rotation of the tube Please provide explanation per line of solution. thanks 10 cm 20 cm B +12.5 cm - 12.5 cm 25 cmarrow_forwardA potential flow model of flow over a circular cylinder is described by the following velocity potential R² $ = U_cms (0) (r + 47) Find the magnitude of the pressure gradient normal to the cylinder surface, at an angle of 30° from the leading edge. The constants are given as U = 8 m/s and R = 2 m, while the density of the fluid is p = 1000 kg m-³. Give your answer in Pa/m to the nearest integer value.arrow_forwardTake the densilty and pressure values at 7km, and then apply Bernoulli equation. I think this is the method to solve the problem,If there any you can proceed with that. Please do it fast ,Very urgent. Question 1: . Consider an airplane flying at a standard altitude of 7 km with a velocity of 300 m/s. At a point on the wing of the airplane, the velocity is 400 m/s. Calculate the pressure at this point.arrow_forward
- Q1: The U tube (in Fig.1) is open at (D) and closed in (A). What will be the pressure at point (A, B and C): 1- Uniform acceleration (az=10m/sec?) to the top only. 2- Uniform acceleration (ax =10m/sec²) to the right and (az=10m/sec") to the top. 0.6m 0.9m Fig.1arrow_forwardAnswer with True or False of the following question: (7M 1. Water flows steadily down a vertical pipe of constant cross section. Neglecting friction, according to Bernoulli's equation, velocity decreases with height. 2. A liquid in an open right circular cylinder is given rigid body rotation about the axis of the cylinder. The pressure distribution in any vertical plane is uniform. 3. A curved surface is submerged in a static liquid. The horizontal component of pressure force on it is equal to the pressure force on a vertical projection of the surface. 4. A U-tube manometer measures the difference in total energy between two points.arrow_forwardIn a wind tunnel lab, the pitot tube is located at the height of 2 m, the measured static pressure P=1.0 Pa, total pressure P₁-88 Pa, if we assume the flow in the test section follow the profile of exponential function with a-0.22. Please calculated the wind velocity at the height of 1m. p=1.22kg/m³. (continued 1) Measured pressures at points A, B and C as follows: P-25 Pa, P=-55 Pa, P=-43 Pa, please calculate the wind pressure coefficients based on the reference wind velocity pressure at 1 m. A Carrow_forward
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