A mass (or load) acting downward on a piston confines a fluid of density ρin a closed container,

step 1 Good day. The topic is about Pascal's principle. Pascal's principle states that change in pressu

A mass (or load) acting downward on a piston confines a...

A mass (or load) acting downward on a piston confines a fluid of density $\rho$ in a closed container, as shown in Fig. $13-2$. The combined weight of the piston and load on the right is $200 \mathrm{~N}$, and the cross-sectional area of the piston is $A=8.0 \mathrm{~cm}^{2}$. Find the total pressure at point- $B$ if the fluid is mercury and $h=25 \mathrm{~cm}\left(\rho_{\mathrm{Hg}}=13\right.$ $600 \mathrm{~kg} / \mathrm{m}^{3}$ ). What would an ordinary pressure gauge read at $B$ ? Recall what Pascal's principle tells us about the pressure applied to the fluid by the piston and atmosphere: This added pressure is applied at all points within the fluid. Therefore, the total pressure at $B$ is composed of three parts: Pressure of the atmosphere $=1.0 \times 10^{5} \mathrm{~Pa}$ Pressure due to the piston and load $=\frac{F_{w}}{A}=\frac{200 \mathrm{~N}}{8.0 \times 10^{-4} \mathrm{~m}^{2}}=2.5 \times 10^{5} \mathrm{P}$ Pressure due to the height $h$ of fluid $=h p g=0.33 \times 10^{5} \mathrm{~Pa}$ In this case, the pressure of the fluid itself is relatively small. We have Total pressure at $B=3.8 \times 10^{5} \mathrm{~Pa}$ The gauge pressure does not in clude atmospheric pressure. Therefore, Gauge pressure at $B=2.8 \times 10^{5} \mathrm{~Pa}$

A mass (or load) acting downward on a piston confines a fluid of density $\rho$ in a closed container, as shown in Fig. $13-2$. The combined weight of the piston and load on the right is $200 \mathrm{~N}$, and the cross-sectional area of the piston is $A=8.0 \mathrm{~cm}^{2}$. Find the total pressure at point- $B$ if the fluid is mercury and $h=25 \mathrm{~cm}\left(\rho_{\mathrm{Hg}}=13\right.$ $600 \mathrm{~kg} / \mathrm{m}^{3}$ ). What would an ordinary pressure gauge read at $B$ ?
Recall what Pascal's principle tells us about the pressure applied to the fluid by the piston and atmosphere: This added pressure is applied at all points within the fluid. Therefore, the total pressure at $B$ is composed of three parts:
Pressure of the atmosphere $=1.0 \times 10^{5} \mathrm{~Pa}$ Pressure due to the piston and load $=\frac{F_{w}}{A}=\frac{200 \mathrm{~N}}{8.0 \times 10^{-4} \mathrm{~m}^{2}}=2.5 \times 10^{5} \mathrm{P}$
Pressure due to the height $h$ of fluid $=h p g=0.33 \times 10^{5} \mathrm{~Pa}$
In this case, the pressure of the fluid itself is relatively small. We have
Total pressure at $B=3.8 \times 10^{5} \mathrm{~Pa}$
The gauge pressure does not in clude atmospheric pressure. Therefore,
Gauge pressure at $B=2.8 \times 10^{5} \mathrm{~Pa}$

Key Concepts

Fluid Pressure

Fluid pressure is the force exerted per unit area by a fluid at rest. This pressure is transmitted uniformly in all directions in a confined fluid and can be calculated as the sum of contributions from various sources, such as atmospheric pressure, additional forces applied on the fluid, and the pressure generated by the fluid's own weight. It plays a fundamental role in hydrostatics and many practical applications, such as hydraulic systems.

Pascal's Principle

Pascal's Principle states that when pressure is applied to a confined fluid, the change in pressure is transmitted undiminished throughout the entire fluid. This principle enables the distribution of forces within hydraulic systems and is essential for understanding how external forces, like those from a load or piston, affect the pressure at different points within the fluid.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the gravitational force acting on it. This part of the total pressure depends on the density of the fluid, gravitational acceleration, and the vertical depth from the surface of the fluid. It is calculated by multiplying the fluid density, gravitational acceleration, and the height of the fluid column, and is crucial for analyzing pressure variations in fluids.

Gauge Pressure vs Absolute Pressure

Gauge pressure is the pressure relative to the ambient atmospheric pressure, meaning it is obtained by subtracting the atmospheric pressure from the absolute pressure. In contrast, absolute pressure is the total pressure within a system, including the atmospheric pressure. This differentiation is important in practical applications where instruments may only measure the pressure in excess of the atmospheric pressure.

Transcript

0:00 Good day.

00:01 The topic is about pascal's principle.

00:03 Pascal's principle states that change in pressure applied to an enclosed fluid is transmitted and diminished to all portions of the fluid and to the walls.

00:12 Suppose we exert a pressure or force at section, the left section of this column here, which is connected to another section which is at the right.

00:22 At point one, pressure that is felt there is equal to the ratio of the force and the area.

00:28 And since according to the passage principle, this pressure is undiminished and transmitted to all parts of the fluid, then at the same level at 0 .2 on the right section of the column, we have the, we must establish the same pressure as that in 1.

00:46 So we say p1 is equal to p2.

00:50 Suppose a certain load of 200 newton is supported by a platform which area is 8 .6.

00:59 Centimeter squared and this is it exerts pressure as a result of this on the fluid which in this case is mercury and has a density of 13 ,600 kilogram meter kilogram per meter cube this load is at the height of our each above section b which is on the other end of the column we wish to find the great gauge pressure that is felt at point b so that let us start by noting that in this column here as a consequence of pascal's principle, at some section say we label c or at some point we say c, the pressure at this point c is the same as the pressure at point b because the pressure that is at point b or at point c is transmitted all the way into the fluid and thus at point b where it is at the same height or level as point c the pressure must be the same so we will establish the pressure at point c because we know that that's also the gauge pressure at point b so at point c there are two pressure at contributing the total pressure at that point namely the pressure that is exerted by the load on the surface of the fluid and also the hydrostatic pressure as the result of the difference in the height so we have b at c is equal to the grade pressure at point c is equal to the pressure by the load plus the pressure due to hydostatic pressure of the column of liquid which is h, which is h depth or with the depth of h.

02:49 So we say h...

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