Question 3 The power, P, to drive an axial pump is in a function of density of fluid, p, volumetric flow rate, Q, pump head, h, diameter of rotor, D, and angular speed of rotor, N. (a) (b) (c) P PDS N3 Verify that - is a dimensionless group. Determine the remaining pi group and perform dimensional analysis. Define geometric similarity and dynamic similarity. Categorize the pi group obtained from part (b) as geometric similarity or dynamic similarity, respectively.

Question 3 The power, P, to drive an axial pump is in a function of density of fluid, p, volumetric flow rate, Q, pump head, h, diameter of rotor, D, and angular speed of rotor, N. (a) (b) (c) P PDS N3 Verify that - is a dimensionless group. Determine the remaining pi group and perform dimensional analysis. Define geometric similarity and dynamic similarity. Categorize the pi group obtained from part (b) as geometric similarity or dynamic similarity, respectively.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

See similar textbooks

Similar questions

When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.
Force F is applied at the tip of a cantilever beam of length L and moment of inertia I Fig. . The modulus of elasticity of the beam material is E. When the force is applied, the tip deflection of the beam is z d.Use dimensional analysis to generate a relationship for zd as a function of the independent variables. Name any established dimensionless parameters that appear in your analysis
The velocity V of propagation of ripples on the surface of a shallow liquid depends on the gravitational acceleration g and the liquid depth h. If Buckingham's Theorem is used to identify the salient dimensionless group(s), how many dimensionless group(s) will be obtained? Number of dimensionless group(s) = 1. {1} (Enter your answer as a number.)
Evaluate the use of dimensionless analysis using the Buckingham Pi Theorem for a given fluid flow system (D4) , where resistance tomotion ‘R’ for a sphere of diameter ‘D’ moving at constant velocity on the surface of a liquid is due to the density ‘ρ’ and the surfacewaves produced by the acceleration of gravity ‘g’. The dimensionless quantity linking these quantities is Ne= Function (Fr). To do thisyou must apply dimensional analysis to fluid flow system given in Figure 1 (P11). PICTURE IS ALSO ATTACHED
The spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin rate is a§ectedby the aerodynamic torque. If the torque depends on áight speed V , density , viscosity , ball diameter D,angular velocity !, and the fuzz height, hf , Önd the important dimensionless variables for this case. Use V ,, and D as your scaling (repeating) variables.
Using II-Theorem method to Express (n) in terms of dimensionless groups.The efficiency (n) of a fan depends upon density (p), and dynamic viscosity (u), of the fluid, angular velocity (@), diameter of the rotator (D), and discharge (Q). Q3/ A petroleum crude oil having a kinematics viscosity 0.0001 m?/s is flowing through the piping arrangement shown in the below Figure,The total mass flow rate is equal 10 kg/s entering in pipe (A) . The flow divides to three pipes ( B, C, D). The steel pipes are schedule 40 pipe. note that the dynamic viscosity 0.088 kg/m.s. Calculate the following using SI units: 1- The type of flow in pipe (A). 2- The mass velocity in pipe (B) GB. 3- The velocity in pipe (D) Up. 4- The Volumetric flow rate in pipe (D) QD. 5- The Volumetric flow rate in pipe (C) Qc. Og = 2o mm Ug = 2UA Perolenm crude oIL A ma = 1o Kg/s O = 5o mm mic = ? Go = 7000 k9/m.s Nate that!- O, = 30 mm. D:0iameter. U:velocity G mass velocity mimass How vate
During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blastwave radius R, air density ρ, and time t. Arrange these variables into single dimensionless group, which we mayterm the blast wave number.
Please solve this problem, Thank you very much! Figure is attached 1. liquids in rotating cylinders rotates as a rigid body and considered at rest. The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ?, fluid density ?, gravitational acceleration ?, and radius ?. Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all the steps.
A tiny aerosol particle of density pp and characteristic diameter Dp falls in air of density p and viscosity u . If the particle is small enough, the creeping flow approximation is valid, and the terminal settling speed of the particle V depends only on Dp, µ, gravitational constant g, and the density difference (pp - p). Use dimensional analysis to generate a relationship for Vas a function of the independent variables. Name any established dimensionless parameters that appear in your analysis.
When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.
The pressure drop AP in flow through pipes per unit length is found to depend on the average velocity u, diameter d, density of the fluid p, and viscosity u. Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenon.
Problem 1: The discharge pressure (P) of a centrifugal pump shown below is a function of flow rate (Q), impeller diameter (D), fluid density (p), and impeller angular speed (12). P = f (Q. D, p. 92). Use the Buckingham pi technique to rewrite this function in terms of dimensionless parameters, 1 g (n₂). P= P(Q,D, Dimensions 2) N= 5 Q. P