9. The drag of a sphere, Fo, in a flowing fluid is a function of the...
Q3. Drag measurements were taken for a 5 cm diameter sphere in water at 20°C to predict the drag force of a 1 m diameter balloon rising in air with standard temperature and pressure. Given kinematic viscosity of water (v) = 10 X 106 m²/s and kinematic viscosity of air (v) = 1.46 X 10-5 m2/s. 1. Perform the Buckingham Pi theorem to generate a relationship for Fo as a function of the independent variables. Assume the drag Fo is...
The drag force Fp on a smooth sphere falling in water depends on the sphere speed V, the sphere density P. the density p and dynamic viscosity of water, the sphere diameter Dand the gravitational acceleration g. Using dimensional analysis with p. V and D as repeating variables, determine suitable dimensionless groups to obtain a reneral relationship between the drag force and the other variables. If the same sphere were to fall through air, determine the ratio of the drag...
Question 1 Drag tests show that the drag of a circular disc placed normally to the free-stream velocity (see Figure 1) is a function of the fluid velocity, Vo, the fluid density, p, the fluid viscosity, ?, the disc diameter, D, the free-stream turbulence root mean square velocity, ums, and the turbulence length scale Lx. Here urms and L. are in m/s and m, respectively. By using the Step-by-step method dimensional analysis, develop the r- groups that could be used...
Fluid Mechanics QUESTION 3 State 2 applications of dimensional analysis. (a) (2 marks) (b) The drag force, Fo acting on a ship is considered to be a function of the fluid density (p) viscosity (H). exavitlg). ship velocity (V), and characteristic length (). Using Buckingham П theorem, determine a set ofsuitable dimensionless numbers to describe the relationship.Fo f(p.H.g.V (4 marks) A 1:60 scale model of a ship is used in a water tank to simulate a ship speed of 10...
3.5 2.5 1.5 0.5 8 10 Model velocity, ft/s Problem Statement: A sphere moving in a fluid experiences a drag force that is known to be a function of the sphere diameter, velocity, density, and viscosity. You performed some lab tests on a 3 inch diameter sphere using a water tunnel. The figure below indicates the results of your model test. For the tests the viscosity of the water was 2.34 10sifi2 and the water density was 1.94slugslfi3. Based on...
10.13. The shear stress, Tw, on a flat surface that is caused by a fluid of density p and vis- cosity u flowing over the surface at a velocity V is given by where Re,- V Re where r is the distance from the upstream end of the flat surface. (a) Use the given shear stress distribution, w(x), to determine the drag force on a flat plate of width W and length L in terms of W, L, V, p,...
5. In Fig. P4.5 the flowing fluid is CO2 at 20°C. Neglect losses. IfPi = 170 kPa and the manometer fluid is Meriam red oil (SG 0.827), estimate (a) P and (b) the gas flow rate in m/h Air: p 20 lbf/in2 abs Po = 14.7 blin2 abs P(4.5) 3. The power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate Ω, the density p, and viscosity...
INFO GIVEN PROBLEM Consider a porous sphere sitting in a pool of stagnant Newtonian fluid (with constant viscosity μ). Liquid with constant viscosity μ is forced out radially from the sphere. Your ultimate goal is to find the velocity profile vi(r) of the liquid outside the sphere. The radius of the sphere is given by R. Assume the flow to be steady state; vo-Vo-0; and neglect gravity. Also, the velocity at the sphere surface is given by v(R)-Vo. Assume steady...
с 79% 251 PM Sat Apr 27 2. A solid sphere of diameter d and density ph falls in a fluid of density p and kinematic viscosity u.The gravitational acceleration is g and the terminal velocity is y (a) Determine the non-dimensionalt o for dependence of the viscosity on the other parameters. (b) If a model sphere with di-d/z is use test, determine the kinematic viscosity of the fluid and the terminal velocity vi that make the problem similar. (25...
please help Question 1 1.1 If the velocity distribution of a fluid flowing over a 1m² flat plate is given by u=l+ y + y, find the m. Assume dynamic viscosity to be y=6x10*(Ns/m”). force acting on a plate at y = [5 marks] 1.2 A 2D velocity field in an incompressible flow was measured by PIV method and determined to follow the following functions u= 2x’ +2y and v=x - 4y. Check whether your measurements are correct at a...