5. The drag force, fd, on a sphere located in a pipe through which a fluid is flowing is to be determinedexperimentally. Assume that the drag is a function of the sphere diameter, d, the pipe diameter, D, thefluid velocity, V, and the fluid density, p. (a) What dimensionless parameters would you use for this prob-lem? (b) Some experiments using water indicate that for d = 0.2in., D = 0.5in, and V = 2ft/s, the dragis 1.5 x 10-3lb. Estimate the drag on a sphere located in a 2 - ft-diameter pipe through which water isflowing with a velocity of 6ft/s. The sphere diameter is such that geometric similarity is maintained. (Ans:31.11b)Sphere

The objective of the question is to determine the drag force on a sphere located in a pipe through…

Answered: 5. The drag force, fd, on a sphere…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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In fluid mechanics, which of the following are true: (a) Fluid mechanics is the branch of science concerned with stationary fluids (b) Fluids like water posses only potential energy (c) The field of fluid mechanics is infinite and endless (d) It is a branch of physics which concerns the study of liquids and the ways in which they interact with forces (e) It is a sience concerned with the response of fluids to forces exerted upon them, (f) the fluid which is in state of rest is called as static fluid and its study is called as statics.
Assume that the wall shear stress, Tw, created when a fluid flows through a pipe (see Figure a) depends on the pipe diameter, D, the flowrate, Q, the fluid density, p, and the kinematic viscosity, v. Some model tests run in a laboratory using water in a 0.2-ft-diameter pipe yield the Tw vs. Q data shown in Figure b. Perform a dimensional analysis and use model data to predict the wall shear stress in a 0.3-ft- diameter pipe through which water flows at the rate of 1.5 ft3/s. 0.7 Diameter = D 0.6 2 0.5 0.4 Model data (a) 0.3 0.2 0.1 0.5 1.5 Flowrate, Q, ft/s (b) Tw Ib/ft2 Wall shear stress, T,, Ib/ft? n * m N -
The pressure coefficient is defined by the ratio between the static pressure difference and the dynamic pressure (pictured): Where P is the static pressure [Pa], P∞ is the reference static pressure [Pa], ρ is the density [kg/m3], and V is the velocity [m/s]. Using the primary dimensions and their units, show that the pressure coefficient is dimensionless.
A2) In order to solve the dimensional analysis problem involving shallow water waves as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on the surface of a liquid is a function of the depth (h), gravitational acceleration (g), fluid density (p), and fluid viscosity (µ). By using this Buckingham Pi Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynolds Number (Re) are the relevant dimensionless parameters involve in this problem. b) Manipulate your Pi (1) products to get the parameter into the following form: pch := f(Re) where Re = Fr = c) If one additional primary variable parameter involve in this proolem such as, temperature (T). Discuss on the Pi (m) products that can be produce and explain why this dimensional analysis is very important in the experimental work.
8.1. An airplane wing of 3 m chord length moves through still air at 15°C and 101.3 kPa at a speed of 320 km/h. A !:20 scale model of this wing is placed in a wind tunnel, and dynamic similarity between model and prototype is desired. (a) What velocity is necessary in a tunnel where the air has the same pressure and temperature as that in flight? (b) What velocity is necessary in a variable-density wind tunnel where absolute pressure is 1 400 kPa and temperature is 15°C? (c) At what speed must the model move through water (15°C) for dynamic similarity?
Using diagrams/ illustrations, discuss the relationship between Dimensional Analysis and Dynamic and Geometric Similarity. You are to include purposes and applications of this principle.?
(b) One form of fluid movement is rotation and deform angularly. Figure Q1(b) shows the rotation and angular deformation caused by velocity variation about z-axis. Based on Table 1 and setting given to you, derive an equation of rotation. ди Sy St ây > B' ĉu B B ôy dy A' ↑ Sa v+. ôx A ôx Figure Q1(b) : Rotation and Angular Deformation Table 1: Axis of Rotation Setting Axis of Rotation 2 у-ахis
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> | E9 docs.google.com/form تبديل الحساب Questions 7 نقاط Q1/ The power of 6-blade flat blade turbine agitator in a tank is a function of diameter of impeller, number of rotations of the impeller per unit time, viscosity and density of liquid. From a dimensional analysis, obtain a relation between the power and the four variables. 3. صفحة 2 من
Ex. The force required to tow a 1:30scale model of a motor boat in a lake at a speed of 2m/s is 0.5 N, Assuming that the viscosity resistance due to water and air is negligible in comparison with the wave resistance, calculate the corresponding speed of the prototype for dynamically similar conditions. What would be the force required to propel the prptype at that velocity in the same lake? Ans.: 10.95m/s, 13500N
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