Q1: The drag force (F) of an aircraft during flight depends upon the length of aircraft L, flow velocity V, air viscosity u, air density p, and bulk modulus of air K. (1) Derive the relationship between the above variables and the drag force by using Buckingham's II- +heorem (2) Evnlein the hysicol meoning of+he htoined dimoncionleg

Q1: The drag force (F) of an aircraft during flight depends upon the length of aircraft L, flow velocity V, air viscosity u, air density p, and bulk modulus of air K. (1) Derive the relationship between the above variables and the drag force by using Buckingham's II- +heorem (2) Evnlein the hysicol meoning of+he htoined dimoncionleg

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 5.13P: 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its...

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01: The drag force (F) of an aircraft during flight depends upon the length of aircraft flow velocity air viscosity density p. and bulk modulus of air K. (1) Derive the relationship between the above variables and the drag force by using Buckingham's II theorem . (2) Explain the physical meaning of the obtained dimensionless groups .
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.
Under a laminar flow, the liquid flows through small holes. It has a triangular cross-section, width b and length L, where the volumetric flow rate Q of the flow is a function of viscosity. ,pressure reduction per unit length p/L and width b 1) Use the PI theory to write the relationship as a dimensionless variable. 2) if the width b is doubled by viscosity And the pressure drop per unit length p/L is the same. I want to know how the flow rate Q will change.
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.
The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 0, and the number of blades n. (a) Write this relationship in dimensionless form. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 r/min. (b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? (c) What is the appropriate rotation rate of the prototype?
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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
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.
1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure 2, and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT = Fr pV2D² = fen (T₁, T₂, ...Tk) What is k? Explain. Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V.
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2- The resistance (R) experienced by a partially submerged body depends upon the velocity (u), length of the body (L), dynamic viscosity (u) and density (p) of the fluid, and gravitational acceleration (g). Obtain a dimensionless expression for (R). Ans. R=(u²L p) f Lg