Let the force acting on the piston be F and the length of the cylinder be l. Then, work done =F

step 1 Hello students in this question we have to find the work done that is required to squeeze all wa

Let the force acting on the piston be F and the length of...

Let the force acting on the piston be $\mathrm{F}$ and the length of the cylinder be $l$. Then, work done $=F l$ Applying Bernoulli's theorem for points $A$ and $B, p=\frac{1}{2} \rho v^{2}$ where $\rho$ is the density and $v$ is the velocity at point $B$. Now, force on the piston, $F=p A=\frac{1}{2} \rho v^{2} A$ where $A$ is the cross section area of piston. Also, discharge through the orifice during time interval $t=S v t$ and this is equal to the volume of the cylinder, i.e., From Eq. (1), (2) and (3) work done $=\frac{1}{2} \rho v^{2} A l=\frac{1}{2} \rho A \frac{V^{2}}{(S t)^{2}} l=\frac{1}{2} \rho V^{3} / S^{3} t^{2}$

Let the force acting on the piston be $\mathrm{F}$ and the length of the cylinder be $l$. Then, work done $=F l$ Applying Bernoulli's theorem for points
$A$ and $B, p=\frac{1}{2} \rho v^{2}$ where $\rho$ is the density and $v$ is the velocity at point $B$. Now, force on the piston, $F=p A=\frac{1}{2} \rho v^{2} A$
where $A$ is the cross section area of piston. Also, discharge through the orifice during time interval $t=S v t$ and this is equal to the volume of the cylinder, i.e.,
From Eq. (1), (2) and (3) work done $=\frac{1}{2} \rho v^{2} A l=\frac{1}{2} \rho A \frac{V^{2}}{(S t)^{2}} l=\frac{1}{2} \rho V^{3} / S^{3} t^{2}$

Key Concepts

Pressure in Fluid Dynamics

Pressure is defined as the force exerted per unit area within a fluid. It plays a key role in determining how fluids behave under various forces, especially in converting energy forms and maintaining the equilibrium of fluid systems.

Force due to Pressure and Area

The force exerted by a fluid on a surface is determined by multiplying the pressure of the fluid by the area over which the pressure is applied. This relationship is essential in understanding how pressure differences can create mechanical forces, such as those on a piston.

Work

Work is the energy transferred to or from an object via the application of force along a displacement. In mechanics, it is calculated as the product of the magnitude of the force and the distance over which that force is applied in the direction of the force.

Bernoulli's Principle

Bernoulli’s principle in fluid dynamics is based on energy conservation for flowing fluids. It relates the pressure, velocity, and elevation in a fluid flow, indicating that an increase in the speed of the fluid occurs concurrently with a decrease in pressure or potential energy.

Continuity Equation and Volume Discharge

The continuity equation for incompressible fluids establishes that the volume flow rate remains constant along a streamline. This concept is used to link the velocity of a fluid with the area through which it flows, thereby connecting the discharge rate to the physical dimensions of the system.

Transcript

Please give Ace some feedback