The spring of the pressure gauge shown in Figure P14.7 has a...

Key Concepts

Area Calculation for a Circular Piston

The area of a circular piston is found using the formula A = ?r², or equivalently A = (?d²)/4, where r is the radius and d is the diameter. This calculation is necessary for determining the surface area on which the fluid’s pressure exerts force, linking the geometric properties of the piston to the resultant force in the system.

Pressure Acting on a Surface

The force exerted by a fluid on a surface is determined by the pressure of the fluid and the area over which it acts, using the relationship F = PA. This concept is key in relating the pressure increase due to depth with the force applied on the piston of the gauge.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the gravitational force acting on it, calculated as P = ?gh, where ? is the fluid density, g is the acceleration due to gravity, and h is the depth. This principle explains how pressure increases with depth in a fluid such as water.

Hooke's Law

Hooke's Law describes the direct proportionality between the force applied to a spring and its resulting displacement, expressed as F = kx, where k is the spring constant and x is the displacement. This concept is crucial for determining how much force is required to compress or extend the spring by a given distance.

Transcript

00:01 Head over the one.

00:02 We are going to find the pressure exerted by a liquid ongwen object and that object is immersed into that liquid.

00:11 For that, we commonly used a device that is known as a pressure gauge device.

00:17 It looks like this.

00:21 Yeah, it has a question here on there will be a small spring inside and water pressure that or whatever force that has given onto the piston due to that fools the spring inside get accomplished all day result in a change in length off the string and that those mainly or commonly known as the hawks law, that is k x force is given by minus k x work a was the spring constant.

00:58 Okay, so we are immersing this pressure gauge device into a water in a leak.

01:06 So what happens when we, in most this pressure getting to the water? the pressure exerted by the water results in the change in length off the spring.

01:18 And to that, we can find ward the pressure exerted by the liquid that is the water.

01:27 So we already have the equation for pressure, as p is equal, do fools by a dia.

01:36 So when we apply the new hooks low force into this immigration, we have efforts equal to minus k eggs by it.

01:48 There's no matter if you neglect the minus sign, it's just to show that it is in the opposite direction off the food.

01:56 Okay, so we have the aggression off the pressure.

02:02 No.

02:03 What are the other factors that are affecting the pressure? we are considering a liquid, and we have to take into consider the density off that particular liquid.

02:15 Here we are taking water as a liquid.

02:19 So the density off water that is 1000 kilogram put me to cuba must be taken into consideration.

02:30 Okay, no, what does the next thing we have to take that is the acceleration due to gravity that is 9.8 meters per second squared.

02:43 And also the pressure changes due to another factor.

02:47 That is the height at which the object is held in that liquid.

02:53 So height is another factor, and that is an unknown factor.

02:59 Tow us for now...