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Bernoulli's Equation

Bernoulli's Equation

In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...

Bernoulli's Equation: Problem Solving

Bernoulli's Equation: Problem Solving

A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity equation is...

Hazard Rate

Hazard Rate

The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...

Bernoulli's Principle: Applications

Bernoulli's Principle: Applications

There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:

Bernoulli's Principle

Bernoulli's Principle

Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to zero. It is also helpful in analyzing horizontal flows in which the gravitational energy density is constant throughout. The latter equation is so useful that it is called Bernoulli's principle. According to Bernoulli's principle, the fluid pressure drops if the speed increases and vice versa.
Bernoulli's principle has several applications. It is used...

Wald-Wolfowitz Runs Test II

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...

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Related Experiment Video

Updated: Jul 10, 2026

Intravital Microscopy of Monocyte Homing and Tumor-Related Angiogenesis in a Murine Model of Peripheral Arterial Disease

Intravital Microscopy of Monocyte Homing and Tumor-Related Angiogenesis in a Murine Model of Peripheral Arterial Disease

Published on: August 26, 2017

Detecting a rate increase using a Bernoulli scan statistic.

Michael D Joner¹, William H Woodall, Marion R Reynolds

¹TechStatistics, Aiken, SC 29803, USA. mjoner@gmail.com

Statistics in Medicine

|October 18, 2007

Summary

This study evaluates prospective scan statistics for public health surveillance. While cumulative sum (CUSUM) methods detect sustained increases better, scan statistics offer a simpler approach for early detection of disease rate changes.

More Related Videos

ScanLag: High-throughput Quantification of Colony Growth and Lag Time

ScanLag: High-throughput Quantification of Colony Growth and Lag Time

Published on: July 15, 2014

Related Experiment Videos

Last Updated: Jul 10, 2026

Intravital Microscopy of Monocyte Homing and Tumor-Related Angiogenesis in a Murine Model of Peripheral Arterial Disease

Intravital Microscopy of Monocyte Homing and Tumor-Related Angiogenesis in a Murine Model of Peripheral Arterial Disease

Published on: August 26, 2017

ScanLag: High-throughput Quantification of Colony Growth and Lag Time

ScanLag: High-throughput Quantification of Colony Growth and Lag Time

Published on: July 15, 2014

Area of Science:

Public Health Surveillance
Biostatistics
Epidemiology

Background:

Scan statistics are established for retrospective disease outbreak detection.
Prospective surveillance methods are needed for timely identification of emerging health threats.
Existing methods often focus on analyzing historical data rather than real-time event occurrences.

Purpose of the Study:

To investigate the performance of scan statistics in prospective public health surveillance.
To evaluate the efficiency of scan statistics for detecting increases in incidence rates over time.
To compare prospective scan statistics with the Bernoulli-based cumulative sum (CUSUM) technique.

Main Methods:

Analysis of prospective scan statistic properties under independent Bernoulli observations.
Evaluation of the expected number of observations required for signal generation.
Comparative performance analysis against the Bernoulli-based cumulative sum (CUSUM) method.

Main Results:

The prospective scan statistic can signal increases in incidence rates.
The Bernoulli-based CUSUM technique demonstrates higher effectiveness in detecting sustained rate increases.
Scan statistics provide a simpler alternative with minimal efficiency loss in certain applications.

Conclusions:

Prospective scan statistics are a viable tool for public health surveillance, particularly for early detection.
The choice between scan statistics and CUSUM depends on specific application needs regarding detection timeliness and sustained increase sensitivity.
Scan statistics offer a practical and efficient option for monitoring disease incidence rates in real-time.