Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation

We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail

A critical review of the experimental data for developed free turbulent shear layers

Experimental shear layer data are reviewed and the results are compared to numerical predictions for three test cases. It was concluded from the study that many, if not most, of the apparent inconsistencies which exist in the interpretation of the experimental data for free shear layers result from confusing data taken in developed turbulent flows with those taken in transitional or developing flows. Other conclusions drawn from the study include the following: (1) The effects of Mach number are more uncertain primarily because of limited data and the absence of any turbulence measurements for supersonic shear layers. (2) The data available for heterogeneous shear layers are not sufficient to clearly establish the effect of density ratio on mixing rate

Ultrasonic resonator energy loss determination (chemical kinetics study).

Ultrasonic resonators are used to study chemical kinetics in liquids (relaxation spectrometry). Resonator loss, proportional to Q-1, is frequently determined from half-power bandwidth (amplitude 3 dB down from peak value); but other methods, in particular those utilising the phase characteristic at resonance, are often advantageous. The author describes three different techniques, employing an AM driving signal for the resonator network, affecting the modulation envelope; a resonance peak compensation (RF amplitude and phase of the output signal); the phase slope (group delay) of the output signal. Relations for the one-dimensional ultrasonic resonator, circuit diagrams and measurement examples are given

Planetary explorer liquid propulsion study

An analytical evaluation of several candidate monopropellant hydrazine propulsion system approaches is conducted in order to define the most suitable configuration for the combined velocity and attitude control system for the Planetary Explorer spacecraft. Both orbiter and probe-type missions to the planet Venus are considered. The spacecraft concept is that of a Delta launched spin-stabilized vehicle. Velocity control is obtained through preprogrammed pulse-mode firing of the thrusters in synchronism with the spacecraft spin rate. Configuration selection is found to be strongly influenced by the possible error torques induced by uncertainties in thruster operation and installation. The propulsion systems defined are based on maximum use of existing, qualified components. Ground support equipment requirements are defined and system development testing outlined

Wyoming

Wyoming currently ranks eighth nationally in both crude oil and natural gas production. In 2018, Wyoming produced 87.9 million barrels of crude oil, up from 75.7 million barrels in 2017. Wyoming produced 1.81 billion MCF (thousand cubic feet) of natural gas, increasing from 1.80 billion MCF produced in 2017

Theory of Drop Formation

We consider the motion of an axisymmetric column of Navier-Stokes fluid with a free surface. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which constitute a unique continuation of the Navier-Stokes equation through the singular point. We calculate the asymptotic solutions of the Navier-Stokes equation, both before and after the singularity. The solutions have scaling form, characterized by universal exponents as well as universal scaling functions, which we compute without adjustable parameters