Buckingham Pi TheoremPropeller thrust (a force) of a boat's motor depends on the diameter and angular velocity of the propellers, the boať's speed, and the density and viscosity of theliquid the boat is in.How many factors of influence need to be considered?How many pi groups are needed if we use F, L, I dimensions?

Answered: Image /qna-images/answer/364414bc-c6a6-4517-bd52-bf1e4c3ab14b.jpg

Buckingham Pi Theorem Propeller thrust (a force) of a boat's motor depends on the diameter and angular velocity of the propellers, the boat's speed, and the density and viscosity of the liquid the boat is in. How many factors of influence need to be considered? How many pi groups are needed if we use F, L, T dimensions?

Buckingham Pi Theorem Propeller thrust (a force) of a boat's motor depends on the diameter and angular velocity of the propellers, the boat's speed, and the density and viscosity of the liquid the boat is in. How many factors of influence need to be considered? How many pi groups are needed if we use F, L, T dimensions?

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...

See similar textbooks

Similar questions

5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
Evaluate the dimensionless groups hcD/k,UD/, and cp/k for water, n-butyl alcohol, mercury, hydrogen, air, and saturated steam at a temperature of 100C. Let D=1m,U=1m/sec, and hc=1W/m2K.
A weir is an obstruction in a channel flow that can be calibratedto measure the flow rate, as in Fig. . The volumeflow Q varies with gravity g , weir width b into thepaper, and upstream water height H above the weir crest. Ifit is known that Q is proportional to b , use the pi theorem tofind a unique functional relationship Q ( g , b , H ).
As a mechanical engineer, you can predict the performance of a new centrifugal pump using two methods which are One Dimensional Analysis (Velocity Triangle) and Hydraulic Scaling. Describe the limitation of each method.
The Archimedes number, Ar, used in the flow of stratifiedfluids, is a dimensionless combination of gravity g , densitydifference Δ ρ , fluid width L , and viscosity μ . Find theform of this number if it is proportional to g .
Figure shows the flow of water over a dam. Thevolume fl ow Q is known to depend only on crest width B ,acceleration of gravity g , and upstream water height Habove the dam crest. It is further known that Q is proportionalto B . What is the form of the only possible dimensionallyhomogeneous relation for this flow rate?
Suppose we know little about the strength of materials butare told that the bending stress σ in a beam is proportionalto the beam half-thickness y and also depends on thebending moment M and the beam area moment of inertiaI . We also learn that, for the particular case M = 2900in ∙ lbf, y = 1.5 in, and I = 0.4 in4 , the predicted stressis 75 MPa. Using this information and dimensional reasoningonly, find, to three significant figures, the onlypossible dimensionally homogeneous formula σ=y f ( M , I ).
When a person ice skates, the surface of the ice actuallymelts beneath the blades, so that he or she skates on a thinsheet of water between the blade and the ice.( a ) Find an expression for total friction force on the bottomof the blade as a function of skater velocity V , bladelength L , water thickness (between the blade and theice) h , water viscosity μ , and blade width W .( b ) Suppose an ice skater of total mass m is skatingalong at a constant speed of V 0 when she suddenlystands stiff with her skates pointed directly forward,allowing herself to coast to a stop. Neglecting frictiondue to air resistance, how far will she travelbefore she comes to a stop? (Remember, she iscoasting on two skate blades.) Give your answer forthe total distance traveled, x , as a function of V 0 , m ,L , h , μ , and W .( c ) Find x for the case where V 0 = 4.0 m/s, m = 100 kg,L = 30 cm, W = 5.0 mm, and h = 0.10 mm. Do youthink our assumption of negligible air resistance is agood one?
Taylor number (Ta) is used here to describe the ratio between the inertia effect andthe viscous effect. By applying Buckingham Pi’s Theorem, determine an equation forTa as a function of the radius of inner cylinder (r), cylinder tangential velocity (v),fluid dynamic viscosity (μ), gap distance (L) and fluid density (ρ).
Fluid mechanics, I need solutions in 15 minutes please. MCQ/Determine the horizontal and vertical components of the liquid pressure acting on the semicylindrical gate ABC, as shown in the figure. The width into the paper is 1 m. A-Fx = 257.430 kN and Fy = 59.801 kN B-Fx = 164.018 KN and Fy = 37.229 KN C-Fx = 269.894 kN and Fy = 65.526 KN D-Fx = 98.182 kN and Fy = 20.002 KN E-Fx = 234.789 kN and Fy = 52.418 kN F-Fx = 187.005 kN and Fy = 42.182 KN G-Fx = 119.956 kN and Fy = 25.550 KN H-Fx = 141.327 kN and Fy = 31.171 KN I-Fx = 288.147 kN and Fy = 69.098 KN J-Fx = 213.112 kN and Fy = 47.903 KN
The terminal velocity of a sphere (maximum drop velocity) depends on sphere diameter (D), sphere density (ρs), fluid density (ρf), fluid viscosity (μ) and acceleration due to gravity (g). By using Buckingham π-Theorem, create a nondimensional form for the terminal velocity. Show all the steps and calc
The thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D, dynamic viscosity , density p. the speed of sound in the medium C. (1) Derive the relationship between the above variables and the thrust force by using Buckingham's IT-theorem. (2) Explain the physical meaning of the obtained dimensionless groups. إجابت