Cnnsider a venturi with a small hole drilled in the side of...

Cnnsider a venturi with a small hole drilled in the side of the throat. This hole is connected via a tube to a closed reservoir. The purpose of the venturi is to create a vacuum in the reservoir when the venturi is placed in an airstream. (The rncunun is defined as the pressure difference helow the outside ambient pressure.) The venturi has a throat-10-inlet area ratio of 0.85 . Calculate the maximum vacuum obainable in the reservoir when the venturi is placed in an airstream of $90 \mathrm{~m} / \mathrm{s}$ at standard sea level conditions.

Key Concepts

Bernoulli's Principle

This fundamental principle in fluid dynamics states that, along a streamline, the sum of the pressure head, velocity head, and elevation head remains constant in a steady, incompressible, and non-viscous flow. In the context of a venturi, the increase in flow velocity through the constricted throat is accompanied by a drop in static pressure. This principle is essential for analyzing the pressure changes that create the vacuum in a reservoir connected to the venturi’s throat.

Venturi Effect

The venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. In this problem, drilling a small hole at the throat, where fluid velocity is highest and pressure is lowest, allows tapping into this low-pressure region to create a vacuum. Understanding this effect is key to designing systems that utilize pressure differences for tasks such as suction or fluid mixing.

Continuity Equation

The continuity equation, which expresses the conservation of mass in a fluid flow, relates the variable cross-sectional areas in a venturi to the velocities at those points. When the area decreases, the fluid velocity must increase to maintain a constant mass flow rate. This relationship is fundamental in determining the velocity distribution within a venturi and, by extension, the pressure drop that produces the vacuum.

Fluid Properties at Standard Sea Level Conditions

Standard sea level conditions provide reference values such as ambient pressure and air density, which are critical for accurately calculating the pressures and velocities in the fluid flow. These values allow for the estimation of dynamic pressure effects when air flows at a given speed, which in this case is necessary for computing the maximum achievable vacuum in the reservoir.

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