The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

A monitoring system and method for monitoring a predetermined set of physical characteristics associated with a structure using the monitoring system. The system is distributed in the structure and comprises a distributed optical sensing device ( 30 ), further comprising a fiber optic cable ( 20, 22 ); a light source ( 18 a ) operatively in communication with the fiber optic cable ( 20, 22 ); a light detection device ( 18 b ), operatively in communication with the fiber optic cable ( 20, 22 ), for measuring the light received at the light detection device ( 18 b ) from the fiber optic cable ( 20, 22 ); and a data processor ( 18 ) capable of using the light measured to calculate a predetermined set of physical parameters describing the predetermined set of physical characteristics.

Method and system for monitoring smart structures utilizing distributed optical sensors

A surgical tool system includes an electrosurgical tool for sealing and transecting tissue and a tactile feedback system integrated onto a handle of the tool that generates relevant feedback in at least the form of haptic effects to the user. The tactile feedback alerts the user of tissue properties, i.e., when tissue located within jaws of the tool is completely sealed, when the tissue is ready to be cut, the cutting rate or speed, the quantity of tissue located within jaws of the tool, and whether a blood vessel is fully located within jaws of tool. In addition, the tactile feedback alerts the user to the operating status of energy application during the procedure.

Electrosurgical sealing tool having haptic feedback

An intelligent well system and method has a sand face completion and a monitoring system to monitor application of a well operation. Various equipment and services may be used. In another aspect, the invention provides a monitoring system for determining placement of a well treatment. Yet another aspect of the invention is an instrumented sand screen. Another aspect is a connector for routing control lines.

Intelligent well system and method

Ultrasonic flowmeters: half-century progress report, 1955-2005.

At least one parameter of at least one fluid in a pipe (12) is measured using a spatial array of acoustic pressure sensors (14, 16, 18) placed at predetermined axial locations x1,x2,x3 along the pipe (12). The pressure sensors (14, 16, 18) provide acoustic pressure signals P1(t), P2(t), P3(t) on lines (20, 22, 24) which are provided to signal processing logic (60) which determines the speed of sound amix of the fluid (or mixture) in the pipe (12) using acoustic spatial array signal processing techniques with the direction of propagation of the acoustic signals along the longitudinal axis of the pipe (12). Numerous spatial array processing techniques may be employed to determined the speed of sound amix. The speed of sound amix is provided to logic (48) which calculates the percent composition of the mixture, e.g., water fraction, or any other parameter of the mixture or fluid which is related to the sound speed amix. The logic (60) may also determine the mach number (MX) of the fluid. The acoustic pressure signals P1(t), P2(t), P3(t) measured are lower frequency (and longer wavelength) signals than those used for ultrasonic flow meters, and thus is more tolerant to inhomogeneities in the flow. No external source is required and thus may operate using passive listening. The invention will work with arbitrary sensor spacing and with as few as two sensors if certain information is known about the acoustic properties of the system.

Fluid parameter measurement in pipes using acoustic pressures

A multiphase flow meter distributed system is disclosed that is capable of measuring phase flow rates of a multiphase fluid. The distributed system includes at least one flow meter disposed along the pipe, an additional sensor disposed along the pipe spatially removed from the flow meter, and a multiphase flow model that receives flow related parameters from the flow meter and the additional sensor to calculate the phase flow rates. The flow meter provides parameters such as pressure, temperature, fluid sound speed and/or velocity of the fluid, and the additional sensor provides a parameter indicative of pressure and or temperature of the fluid. Depending on production needs and the reservoir dimensions, the distributed system may utilize a plurality of flow meters disposed at several locations along the pipe and may further include a plurality of additional sensors as well. The distributed system preferably uses fiber optic sensors with bragg gratings. This enables the system to have a high tolerance for long term exposure to harsh temperature environments and also provides the advantage of multiplexing the flow meters and/or sensors together.

Distributed sound speed measurements for multiphase flow measurement

An apparatus for use in an industrial process for measuring a velocity of a fluid moving in a pipe includes a probe disposed in said fluid flow. The probe includes a tube and an array of at least two sensors disposed at different axial locations along the tube. Each sensor measures inhomogeneous pressure disturbances at respective axial locations. Each sensor further provides a pressure signal. The apparatus also includes a signal processor, responsive to the pressure signals, to provide a signal indicative of the velocity of the fluid. In one embodiment, the sensors filter out wavelengths above a predetermined wavelength. At least one of the sensors comprises a strain gage disposed on a surface of the pipe. In one embodiment, the strain gage comprises a fiber optic strain gage. The apparatus may be configured to detect the velocity of any desired inhomogeneous pressure field in the flow.

Flow rate measurement for industrial sensing applications using unsteady pressures

Non-intrusive pressure sensors (14-18) for measuring unsteady pressures within a pipe (12) include an optical fiber (10) wrapped in coils (20-24) around the circumference of the pipe (12). The length or change in the length of the coils (20-24) is indicative of the unsteady pressure in the pipe. Bragg gratings (310-324) impressed in the fiber (10) may be used having reflection wavelength μ that relate to the unsteady pressure in the pipe. One or more of sensors (14-18) may be axially distributed along the fiber (10) using wavelength division multiplexing and/or time division multiplexing.

Non-intrusive fiber optic pressure sensor for measuring unsteady pressures within a pipe

An apparatus for non-intrusively sensing fluid flow within a pipe is provided. The apparatus includes a first sensing array for sensing acoustic signals traveling at the speed of sound through fluid flow within the pipe, a second sensing array for sensing local pressure variations traveling with the fluid flow, and a housing attached to the pipe for enclosing the sensing arrays. The first sensing array includes a plurality of first optical pressure sensors and the second sensing array includes a plurality of second optical pressure sensors.

Daniel L. Gysling

Papers

Fluid parameter measurement in pipes using acoustic pressures

Distributed sound speed measurements for multiphase flow measurement

Flow rate measurement for industrial sensing applications using unsteady pressures

Non-intrusive fiber optic pressure sensor for measuring unsteady pressures within a pipe

Apparatus for sensing fluid in a pipe