Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to outward centrifugal forces.

Pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.

The pressure difference depends on the fluid's velocity and the sharpness of the curve.

The pressure difference is small for nearly straight streamlines but becomes more pronounced in sharply curved flows, such as vortices or pipe bends.

In practical applications, this concept aids in designing hydraulic structures, curved channels, and pipe systems, where incorrect pressure calculations may lead to structural failure.

It also applies to wind flows around civil structures like buildings and bridges, where pressure differences caused by curved streamlines must be considered to ensure stability.

In the design of curved dams and reservoirs, where water flows along curved surfaces, pressure differences across the streamlines ensure the structure can withstand the forces exerted by the water, especially in high-velocity flows.