A hand-driven tire pump has a piston with a 2.50-cm diameter and a maximum stroke of 30.0 cm . (

step 1 So let's first find the area of piston. Area is pi d squared by 4. D is diameter. Pi times, sinc

A hand-driven tire pump has a piston with a 2.50-cm diameter...

A hand-driven tire pump has a piston with a $2.50-\mathrm{cm}$ diameter and a maximum stroke of 30.0 $\mathrm{cm}$ . (a) How much work do you do in one stroke if the average gauge pressure is $2.40 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ (about 35 $\mathrm{psi} ) ?$ (b) What average force do you exert on the piston, neglecting friction and gravitational force?

A hand-driven tire pump has a piston with a $2.50-\mathrm{cm}$ diameter and a maximum stroke of 30.0 $\mathrm{cm}$ . (a) How much work do you do in one stroke if the average gauge pressure is
$2.40 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ (about 35 $\mathrm{psi} ) ?$ (b) What average force do you exert on the piston, neglecting friction and gravitational force?

Key Concepts

Pressure

Pressure is defined as the force exerted per unit area and is given by the relationship P = F/A. In fluid mechanics, it is a fundamental concept used to describe how forces are distributed within a fluid. Gauge pressure refers to the pressure measured relative to ambient atmospheric pressure and is used extensively in practical applications like tire pumps to account only for the excess pressure.

Work (Pressure-Volume Work)

Work in the context of fluid mechanics is the energy transferred when a fluid is compressed or expanded. It can be computed as the product of pressure and the change in volume (W = P?V) when the pressure is constant. This concept is crucial for determining the mechanical energy input required to perform tasks like pumping air.

Force

Force is an influence that causes an object to undergo a change in motion and is related to pressure by the equation F = PA, where A is the area over which the pressure is applied. In practical scenarios, such as operating a piston in a pump, knowing the relationship between pressure and force helps in understanding how much effort is required to move the piston.

Piston Geometry and Area Calculation

The area of the piston, which is typically circular, is calculated using the formula A = ?r², where r is the radius of the piston. This geometric calculation is essential in problems dealing with pressure and force because the area directly impacts the magnitude of the force produced for a given pressure.

Stroke and Volume Change

The stroke of the piston refers to the distance the piston moves, which determines the volume change (?V) in the system, calculated as the product of the piston area and the stroke length. Understanding the relationship between the stroke length and the change in volume is key to calculating the work done during one pumping cycle.

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