Name: hydrostatic force on dam walls with integration
Uploaded: 2026-01-12T12:24:31.000Z
Duration: 1 min 30 s
Channel: JoVE

La presión hidrostática surge del peso del fluido en reposo y aumenta proporcionalmente con la profundidad.Para una superficie horizontal sumergida a una profundidad fija, la presión es constante y es igual al producto de la densidad del fluido, la aceleración debida a la gravedad y la profundidad.Pero para una superficie vertical como la cara de una presa, cada punto se encuentra a una profundidad diferente, lo que provoca que la presión aumente con la profundidad y crea una distribución de fuerzas no uniforme.Para calcular la fuerza hidrostática total a partir de esta presión variable, la sección sumergida se divide en finas franjas horizontales. Cada tira se encuentra a una profundidad específica y tiene un área igual a su anchura por un pequeño grosor vertical.La presión en cada tira es igual a la densidad de peso del fluido multiplicada por su profundidad bajo la superficie, y la fuerza sobre esa tira es igual a la presión multiplicada por el área.Sumar estas fuerzas en todas las tiras aproxima la fuerza total usando una suma de Riemann. A medida que el grosor de la tira se acerca a cero, la suma se convierte en una integral definida.Esta integral expresa la fuerza hidrostática total como presión multiplicada por la función de anchura, integrada sobre la profundidad sumergida.Este método es esencial en ingeniería civil para diseñar estructuras de contención eficientes.

aplicaciones de la integración para calcular la presión hidrostática

Applications of Integration to Find Hydrostatic Pressure

La fuerza hidrost&#xE1;tica es la fuerza total que ejerce un fluido en reposo sobre una superficie. Para una superficie horizontal sumergida a una profundidad fija, la presi&#xF3;n es constante y se calcula como el producto de la densidad del fluido, la aceleraci&#xF3;n debida a la gravedad y la profundidad. En el caso de un muro vertical de presa sumergido en agua, esta fuerza no se distribuye uniformemente debido al incremento de presi&#xF3;n con la profundidad. Esta variaci&#xF3;n se debe al peso acumulado del agua sobre cada punto. La integraci&#xF3;n se utiliza para considerar el cambio continuo de presi&#xF3;n a lo largo de la superficie sumergida y as&#xED; calcular con precisi&#xF3;n la fuerza hidrost&#xE1;tica total.La presi&#xF3;n en un fluido en reposo aumenta linealmente con la profundidad. A una profundidad h, la presi&#xF3;n P viene dada por:\begin{equation*}P=\rho gh\end{equation*}&#xA0;donde &#x3C1; es la densidad del fluido y g es la aceleraci&#xF3;n debida a la gravedad.Para calcular la fuerza total, la superficie sumergida se divide en franjas horizontales infinitesimales. Cada franja a la profundidad h tiene una anchura w(h) y una altura diferencial dh, por lo que su &#xE1;rea es w(h)dh. La fuerza diferencial dF sobre esa franja es:\begin{equation*}dF=P( \text{area})=(\rho gh)( w(h)dh)\end{equation*}&#xA0;Sumando las fuerzas sobre todas estas franjas desde a hasta b, la fuerza hidrost&#xE1;tica total F se expresa como la integral definida:\begin{equation*}F=\int_a^b\rho gh w(h)dh\end{equation*}&#xA0;Esta formulaci&#xF3;n considera las variaciones en el ancho del muro de presa con la profundidad, lo que permite un modelado preciso de superficies planas y curvas.Este m&#xE9;todo es esencial en campos de la ingenier&#xED;a como la civil y la hidr&#xE1;ulica. Garantiza el dise&#xF1;o seguro y eficaz de estructuras como presas, muros de contenci&#xF3;n, compuertas y tanques de almacenamiento al calcular c&#xF3;mo la presi&#xF3;n variable del fluido afecta a la integridad estructural. La capacidad de la integraci&#xF3;n para representar con exactitud la distribuci&#xF3;n de la fuerza proporciona a los ingenieros la precisi&#xF3;n necesaria para la estabilidad y la seguridad en estructuras en contacto con fluidos.El c&#xE1;lculo fundamenta las pr&#xE1;cticas modernas de ingenier&#xED;a al transformar las leyes f&#xED;sicas en expresiones integrables. Permite el an&#xE1;lisis y la construcci&#xF3;n de sistemas complejos del mundo real.

Aplicaciones de la integración para calcular la presión hidrostática

La fuerza hidrost&#xE1;tica es la fuerza total que ejerce un fluido en reposo sobre una superficie. Para una superficie horizontal sumergida a una ...

applications-of-integration-to-find-hydrostatic-pressure

Education

Educación

JoVE Core

Calculus

Cálculo

Unit

Unidad

Application of Techniques of Integration

Aplicación de Técnicas de Integración

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

hydrostatic force on dam walls with integration

Hydrostatic force is the total force a fluid at rest exerts on a surface. For a horizontal surface at a fixed depth, the pressure is constant. It is found by multiplying fluid density, gravitational acceleration, and depth.

A vertical dam wall is different because pressure increases with depth. The water above each point adds to the pressure below it. That means the force is not spread evenly across the wall.

Integration helps measure this changing force. Pressure in a still fluid rises linearly with depth. At depth h, the pressure P depends on the fluid density ρ and gravity g.

To find the total force, the submerged surface is split into very thin horizontal strips. Each strip has width w(h) and small height dh, so its area is w(h)dh. The force on one strip is written as a differential force dF.

The forces on all strips are added with a definite integral from depth a to depth b. This method also works when the wall width changes with depth. It can model both flat and curved surfaces.

These calculations matter in civil and hydraulic engineering. Engineers use them to design dams, retaining walls, gates, and storage tanks safely. Integration gives the precision needed to handle changing fluid pressure and protect structural integrity.

Hydrostatic Force on Dam Walls with Integration

hydrostatic-force-on-dam-walls-with-integration

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applications of integration to find hydrostatic pressure

Hydrostatic force is the total force a fluid at rest exerts on a surface. For a horizontal surface at a fixed depth, the pressure is constant. It is found by multiplying fluid density, gravitational acceleration, and depth. A vertical dam wall is different because pressure increases with depth. The water above each point adds to the pressure below it. That means the force is not spread evenly across the wall. Integration helps measure this changing force. Pressure in a still fluid rises...

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key terms and concepts

Learn how integration is used to calculate hydrostatic force on dam walls by adding the changing pressure of water across submerged surfaces.

Hydrostatic Force on Dam Walls with Integration | JoVE K12

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calculus

Hydrostatic Force on Dam Walls with Integration

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