Some Dynamical Characteristics of Propellers

1934 ◽  
Vol 38 (288) ◽  
pp. 987-997
Author(s):  
J. Morris
Keyword(s):  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Dynamical Characteristics ◽  
Perpendicular Distance ◽  
Rigid Rod

Referring to Fig. 1, let xOy be the plane of rotation of a rigid rod AOA' consisting of a series of pairs of masses symmetrically disposed about O. Thus at a distance r on either side of O are masses mr. Let AOA' rotate with uniform angular velocity Ω, about the axis Oz and let the plane xOy simultaneously rotate about the axis Ox, supposed fixed in space, with constant angular velocity w. Let ρ be the perpendicular distance mrMr of mr to the axis Ox.

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

The Swimming of Nymphon Gracile (Pyconogonida)

1971 ◽  
Vol 55 (1) ◽  
pp. 273-287
Author(s):  
ELFED MORGAN
Keyword(s):  
Angular Velocity ◽  
Hydrodynamic Force ◽  
Beat Frequency ◽  
High Elevation ◽  
Dorsal Side ◽  
Constant Angular Velocity ◽  
Power Stroke ◽  
Lateral Thrust ◽  
Constant Depth ◽  
Recovery Stroke

1. The organization of the swimming legs of N. gracile has been described. The legs beat ventrally so the animal swims with the dorsal side foremost. The joints between the major segments of the leg are extended for most of the power stroke, but the distal segments articulate sequentially later in the beat, commencing with the flexion of the femoro-tibial joint at the end of the power stroke. Continued flexion reduces the leg radius considerably during the recovery stroke. 2. Animals swimming at constant depth were found to have a leg-beat frequency of about 1 beat/s. Above this the rate of ascent increased rapidly with increasing frequency of beat. Abduction or adduction of the leg usually occurred prior to the start of the power stroke with the femur in the elevated position. 3. Assuming a fixed limb profile at constant angular velocity, maximum lift was calculated to have occurred with the femur inclined at an angle of about 50° to the dorso-ventral body axis. The outward component of the lateral thrust decreased to zero at this point, and with further declination of the femur the lateral forces became inwardly directed. Of the different segments of the leg, tibia 2 and the tarsus and propodium contribute most of the hydrodynamic force. 4. The angular velocity of the leg varied during the power stroke, and the actual forces generated during two beats having the same amplitude and angular velocity but of high and low elevation were calculated. Greater lift occurred during the high-elevation beat when the leg continued to provide lift throughout the power stroke, whereas the low-elevation beat acquired negative lift values towards the end of the power stroke. The lateral thrust was now directed entirely inwards.

The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

2018 ◽  
Vol 277 ◽  
pp. 168-177
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Temperature Field ◽  
Dirichlet Problem ◽  
Heat Exchange ◽  
Angular Velocity ◽  
Integral Transformation ◽  
Mathematic Model ◽  
Constant Angular Velocity ◽  
Temperature Fields ◽  
Finite Velocity ◽  
Finite Space

It is the first generalized 3D mathematic model, which is created for calculating temperature fields in the empty isotropic rotary body, which is restricted by end surfaces and lateral surface of rotation and rotates with constant angular velocity around the axis OZ, with taking into account finite velocity of the heat conductivity in the form of the Dirichlet problem. In this work, an integral transformation was formulated for the 2D finite space, with the help of which a temperature field in the empty isotropic rotary body was determined in the form of convergence series by the Fourier functions.

Inertial oscillations in a rigid axisymmetric container

1977 ◽  
Vol 358 (1692) ◽  
pp. 17-30 ◽  
Keyword(s):  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Axial Plane ◽  
Axial Distance ◽  
Free Oscillations ◽  
Inertial Oscillations ◽  
Characteristic Cone ◽  
Characteristic Cones

Free oscillations of a fluid rotating with constant angular velocity Ω in a rigid axisymmetric container are considered. Approximations are sought for modes that vary rapidly in each axial plane, on the premise that the pressure at the axis varies with axial distance z as Re [A( z )e iino(z )], where n ≫ 1, o' is real, and A (z) and o (z) >do not vary rapidly with z The pattern made by the characteristic cones of Poincaré’s equation after repeated reflexions at the boundary proves pertinent. Modes are evaluated, with a proportional error o(n -1 ), for a class of containers that has special symmetries and for eigenfrequencies that produce reflexion patterns with topologies like those found in a sphere. The largest velocities in the modes considered occur near the circles where a characteristic cone touches a boundary.

SIFs for Radial Cracks in Annular Discs Under Internal and External Shrinkage Pressure and Constant Angular Velocity

2007 ◽  
Author(s):  
A. Sakhaee-Pour ◽  
A. R. Gowhari-Anaraki ◽  
S. J. Hardy
Keyword(s):  
Finite Element ◽  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Coefficient Of Determination ◽  
Linear Elastic ◽  
Crack Configuration ◽  
Wide Range ◽  
Elastic Fracture ◽  
Radial Cracks

Finite element method has been implemented to predict stress intensity factors (SIFs) for radial cracks in annular discs under constant angular velocity. Effects of internal and external uniform pressure on the SIFs have also been considered. Linear elastic fracture mechanics finite element analyses have been performed and results are presented in the form of crack configuration factors for a wide range of components and crack geometry parameters. These parameters are chosen to be representative of typical practical situations. The extensive range of crack configuration factors obtained from the analyses is then used to develop equivalent prediction equations via a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤ R2 ≤ 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. These equations for the SIFs enable designers to predict fatigue life of the components easily.

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