Hydrostatic Pressure
Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity. It is directly proportional to the depth of the fluid and the density of the liquid. This concept is important in mathematics for understanding fluid dynamics and is often used in calculations related to fluid pressure and buoyancy.
7 Key excerpts on "Hydrostatic Pressure"
- Melvyn Kay(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...Chapter 2 Water standing still Hydrostatics 2.1 INTRODUCTION Hydrostatics is the study of water when it is not moving; it is standing still. It is important to civil engineers who are designing water storage tanks and dams. They want to work out the forces that water creates in order to build reservoirs and dams that can resist them. Naval architects designing submarines want to understand and resist the pressures created when they go deep under the sea. The answers come from understanding hydrostatics. The science is simple both in concept and in practice. Indeed, the theory is well established and little has changed since Archimedes (287–212 BC) worked it out over 2000 years ago. 2.2 PRESSURE The term pressure is used to describe the force that water exerts on each square metre of some object submerged in water, that is, force per unit area. It may be the bottom of a tank, the side of a dam, a ship or a submerged submarine. It is calculated as follows: pressure = force area. Introducing the units of measurement pressure (kN/m 2) = force (kN) area (m 2). Force is in kilo-Newtons (kN), area is in square metres (m 2) and so pressure is measured in kN/m 2. Sometimes pressure is measured in Pascals (Pa) in recognition of Blaise Pascal (1620–1662) who clarified much of modern day thinking about pressure and barometers for measuring atmospheric pressure. 1 Pa = 1 N/m 2. One Pascal is a very small quantity and so kilo-Pascals are often used so that 1 kPa = 1 kN/m 2. Although it is in order to use Pascals, kN/m 2 is the measure of pressure that engineers tend to use and so this is used throughout this text (see example of calculating pressure in Box 2.1). 2.3 FORCE AND PRESSURE ARE DIFFERENT Force and pressure are terms that are often confused...
eBook - ePub- William S. Janna(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
...2 Fluid Statics In this chapter, we study the forces present in fluids at rest. Knowledge of force variations—or, more appropriately, pressure variations—in a static fluid is important to the engineer. Specific examples include water retained by a dam or bounded by a levee, gasoline in a tank truck, and accelerating fluid containers. In addition, fluid statics deals with the stability of floating bodies and submerged bodies and has applications in ship hull design and in determining load distributions for flat-bottomed barges. Thus, fluid statics concerns the forces that are present in fluids at rest, with applications to various practical problems. After completing this chapter, you should be able to: Discuss pressure and pressure measurement; Apply the hydrostatic equation to manometers; Develop equations for calculating forces on submerged surfaces; Examine problems involving stability of partially or wholly submerged objects. 2.1 PRESSURE AND PRESSURE MEASUREMENT Because our interest is in fluids at rest, let us determine the pressure at a point in a fluid at rest. Consider a wedge-shaped particle exposed on all sides to a fluid as illustrated in Figure 2.1a. Figure 2.1b is a free-body diagram of the particle cross section. The dimensions Δ x, Δ y, and Δ z are small and tend to zero as the particle shrinks to a point. The only forces considered to be acting on the particle are due to pressure and gravity. On either of the three surfaces, the pressure force is F = pA. By applying Newton’s second law in the x - and z -directions, we get, respectively, FIGURE 2.1 A wedge-shaped. particle. ∑ F x = p x Δ z Δ y − p s Δ s Δ y sin θ = ρ 2 Δ x Δ y Δ z a x = 0 ∑ F z = p z Δ x Δ y − p s Δ s Δ y cos θ − ρ g Δ x Δ y Δ z 2 = ρ 2 Δ x Δ y Δ z a z = 0 where p x, p z,. and p s are average pressures acting on the three corresponding faces a x and a z are the accelerations ρ is the particle density The net force equals zero in a static fluid...
- Amithirigala Widhanelage Jayawardena(Author)
- 2021(Publication Date)
- CRC Press(Publisher)
...Chapter 3 Fluid statics 3.1 Introduction Fluid statics refers to the mechanics of a fluid at rest. The main concerns in fluid statics are the pressure variation in a fluid at rest and the forces on various objects immersed in a fluid. Forces include body forces and surface forces. Body forces are forces developed without physical contact and distributed over the volume of the fluid. Examples include gravitational and electromagnetic forces. Surface forces are forces acting on the boundaries of a fluid through direct contact such as shear forces and normal forces. In a fluid at rest, there are no shear forces. The only surface force is, therefore the pressure force. Pressure is a scalar quantity and in general varies from point to point as a function of the position co-ordinates as p = p (x, y, z) (3.1) The pressure at any two (or more) points at the same horizontal elevation of the same fluid is the same (Pascal’s law). The pressure variation in the vertical direction is given by ∂ p ∂ z = − ρ g ; o r, p = − ρ g z (3.2) The negative sign indicates that pressure is decreasing with increasing z (z measured positive upwards). In Fluid Mechanics, it is more common to express pressure as p ρ g which is a height (depth, head). Net pressure force resulting from pressure variations can be obtained by summation of forces acting on the fluid element. When pressure acts upon an area, it gives rise to a pressure force. Area is a vector quantity, and the area vector points in a direction normal to the area and its magnitude is equal to the magnitude of the area. Pressure force is a vector and is considered positive when acting inwards, producing a compressive stress. 3.2 Basic equations of fluid statics Considering a fluid element at rest as shown in Figure 3.1, the only forces to be considered are the pressure forces and body forces. Resolving forces in the three directions, x, y and z, they take the form Figure 3.1 Definition sketch for pressures and forces acting on a fluid...
eBook - ePub- Richard Gentle, Peter Edwards, William Bolton(Authors)
- 2001(Publication Date)
- Newnes(Publisher)
...Clearly the simple equation above cannot be used without some modification because we need to take into account the fact that pressures will act in different directions at different points on a curved surface. (Hydrostatic Pressure always acts perpendicularly to the immersed surface, so as the surface curves around then the direction of the perpendicular must also change.) This sounds as though we are going to need to employ some fairly complicated integration to add up the effect of the variation of pressure with depth and direction, but fortunately there are some short cuts we can take to make this into quite a simple problem. Resolving the force on a curved surface (Figure 3.1.22) The key to this simple treatment is the resolution of the total force into horizontal and vertical components which we can then treat completely separately. Suppose we have the problem of calculating the total hydrostatic force acting on a large dam wall holding the water back in a reservoir. Figure 3.1.22 Forces on a curved surface We are looking for the single force F which represents the sum of all the little forces acting over all the dam wall. We can find this if we can calculate separately the horizontal and vertical forces acting on the wall due to the water. Let us begin with the vertical force. Vertical force component The vertical force caused by a static liquid which has a free surface open to the atmosphere results solely from gravity. In other words, the vertical force on this dam wall is simply the weight of the water pressing down on it. Clearly we only need to consider any water which is directly above any part of the wall, i.e. in the volume BCD, since gravity always acts vertically...
eBook - ePubIntroduction to Engineering Mechanics
A Continuum Approach, Second Edition
- Jenn Stroud Rossmann, Clive L. Dym, Lori Bassman(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
...The pressure p = p (z) only, and its dependence is given by d p d z = − ρ g. (16.12) To use this equation to calculate pressure throughout a fluid, it is necessary to specify how the product (ρ g) varies with z. In most engineering applications, variation in g is negligible, and so we concern ourselves primarily with the variation of density ρ. An incompressible fluid is defined as one which requires a very large pressure change to effect a small change in volume. This threshold is so high that in most cases, the fluid’s volume and therefore its density are constant. Most liquids satisfy this requirement. When ρ g can be taken to be constant, the equation for p is easily integrated: ∫ p 1 p 2 d p = − ρ g ∫ z 1 z 2 d z. (16.13) So, p 1 − p 2 = ρ g (z 2 − z 1), (16.14) or, if h = z 2 − z 1, then p 1 − p 2 = ρ gh or p 1 = p 2 + ρ g h. (16.15) This equation describes what is called a Hydrostatic Pressure distribution. The distance h = z 2 − z 1 is measured downward from the location of p 2. Equation 16.15 is sometimes written in the shorthand form: Δ p = ρ g Δ h. (16.16) While Equation 16.16 is handy, we must be mindful of the physical significance of these “deltas.” Hydrostatic Pressure increases linearly with depth, as the pressure increases to “hold up” the weight of the fluid above it. This is familiar knowledge to anyone who has lingered near the bottom of a deep swimming pool, or gone SCUBA diving. Many devices exploit the Hydrostatic Pressure distribution. The hydraulic brakes in an automobile take advantage of the fact that pushing on a column of fluid with a certain force (by pressing on a foot pedal) transmits the pressure by moving brake fluid through the car’s brake lines...
- W. David Yates(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
...16 Hydrostatics and Hydraulics In preparing for the Associate Safety Professional/ Certified Safety Professional examinations, the candidate must have a fundamental understanding of hydraulics and hydrostatics. In the everyday “safety world,” you may not automatically understand the importance of having this understanding. However, if you just take a look around, you will see that having this knowledge can make a difference in the safety and health of employees. A question you may be asking yourself is “What are hydrostatics and hydraulics?” Hydrostatics, also known as fluid statics, is the science of fluids at rest and is a subfield within fluid mechanics. It embraces the study of the conditions under which fluids are at rest in stable equilibrium. Hydrostatics is about the pressures exerted by a fluid at rest. Any fluid is meant, not just water. 1 The use of fluid to do work is called hydraulics, and the science of fluids in motion is fluid dynamics. Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. The study of hydrostatics and hydraulics goes back many centuries to early civilization. Early engineers and scientists succeeded in making water flow from one location to another. The problems they encountered usually involved hydraulics in the pipe flow. Whenever velocity, flow direction, or elevation changes in liquids, forces and pressures are produced. Water Properties Water, or wastewater, weighs 8.34 lb/gal. There are 7.48 gal/ft 3 ; therefore, 1 ft 3 of water will weigh 62.4 lb (8.34 lb/gal × 7.48 gal/ft 3 = 62.4 lb/ft 3). When using metric units, the weight of water is 9.8 kN/m 3. Another important property of water related to the study of hydraulics is the pressure exerted on a column of water. One foot of water height is approximately equal to 0.434 pounds per square inch (psi)...
eBook - ePub- P.K. Jayasree, K Balan, V Rani(Authors)
- 2021(Publication Date)
- CRC Press(Publisher)
...In Hg are typically used barometric pressure. Torr : This is the pressure exerted by a one millimeter tall circle column of mercury. It is also known as millimeter of mercury (mmHg). It is equal to 1/760 atmospheres. atm (Standard atmosphere) : This is a unit of pressure defined as 101,325 Pa (1.01325 bar). It is sometimes used as a reference or standard pressure. It is approximately equal to the atmospheric pressure at sea level. 12.1.3 Pascal’s Law Pascal’s law states that “the intensity of pressure at any point in a fluid at rest is the same in all direction.” If p x = intensity of horizontal pressure on the element of the liquid, p y = intensity of vertical pressure on the element of the liquid, p z = intensity of pressure on the diagonal of the triangular element of the liquid, and θ = angle of the triangular element of the liquid (Figure 12.2), according to Pascal’s law FIGURE 12.2 Forces on a fluid element. p x = p y = p z (12.1) This applies to fluid at rest. 12.1.4 Measurement of Pressure In a stationary fluid the pressure is exerted equally in all directions and is referred to as the static pressure. In a moving fluid, the static pressure is exerted on any plane parallel to the direction of motion. If the fluid is flowing in a circular pipe, the measuring surface must be perpendicular to the radial direction at any point. The pressure connection, which is known as a piezometer tube (Figure 12.3), should be flush with the wall of the pipe so that the flow is not disturbed. FIGURE 12.3 Piezometer. Manometer is a device for measuring fluid pressure consisting of a bent tube containing one or more liquid of different specific gravities. In using a manometer, generally a known pressure (which may be atmospheric) is applied to one end of the manometer tube and the unknown pressure to be determined is applied to the other end...
