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Relation Between Pressure and Velocity is inversely proportional. The lower the pressure exerted by a fluid (liquid or gas) the higher its velocity. Bernoulli's Principle is another name for this. Bernoulli’s principle for pressure and velocity relation can be applied to different types of fluid flow. The motion of the fluid molecules causes fluid pressure. Bernoulli's equation in its simplest form is only relevant to the flow of incompressible and non-viscous fluids.
Also Read: Thermodynamics
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Key Terms: Pressure, Velocity, Molecules, Acceleration, Fluid, Gas
What is Pressure?
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Pressure is defined as a measure of the force applied over a unit area. It is generally expressed in Pascal units (Pa), newtons per square meter (N/m² or kg·m/s²), or pounds per square inch. Few other units used for pressure include the torr, bar, atmosphere (atm), and meters seawater (MSW).
Pressure is represented by the capital letter P or the lowercase letter p in equations.
What is Pressure?
Pressure is a derived unit that is usually expressed in the following units:
P = F / A
Here:
- Pressure is P
- Force is F
- Area is A
The quantity of pressure is scalar. It has a magnitude but not a direction. Pressure is usually a positive number. Negative pressure, on the other hand, is also a possibility.
| Frequently Asked Questions Ques. What is a simple definition of pressure? (1 Mark) Ans. Pressure refers to the perpendicular force per unit area, or the stress at a point within a confined fluid. A firm push on a small area creates high pressure, while a weak push spread out over a large area creates less pressure. Ques. Give the SI Unit of Pressure. (1 Mark) Ans. The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N/m2, or kg·m−1·s−2). Ques. What are the 5 units of pressure? (1 Mark) Ans. The SI unit for pressure is pascals (Pa). Other units of pressure include Torr, Barr, Atm, AT, BA, PSI, and manometric units like mm Hg and FSW. |
Definition of Velocity
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A vector measurement of the rate and direction of motion is defined as velocity. Simply put, velocity refers to how fast something moves in one direction. Velocity may be used to calculate the speed of a particular object.
What is Velocity?
The formula for determining the constant velocity of an entity traveling in a straight line:
r = d / t
Here,
- Speed (sometimes denoted as v for velocity) is denoted by r
- Distance traveled is denoted by the letter d.
- Time it takes to execute a movement is called t
| Frequently Asked Questions Ques. What is the SI Unit of Velocity? (1 Mark) Ans. SI unit of velocity is meter per second (m/s). Also, the velocity magnitude can also be expressed in centimeters per second (cm/s). Ques. What is the symbol of velocity? (1 Mark) Ans. Velocity is a vector with symbol v (boldface). Average values get a bar over the symbol. Displacement is calculated along the shortest path between two points and its magnitude is always less than or equal to the distance. Ques. Can velocity be negative? (2 Marks) Ans. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a positive acceleration). |
Relation Between Pressure and Velocity
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Pressure and Velocity are inversely proportional to each other. When pressure rises, velocity falls, preserving the algebraic total of potential energy, kinetic energy, and pressure. When velocity increases, pressure decreases in a similar way.
Velocity is the speed of an object moving in a particular direction. The velocity of an object can be zero. Pressure is defined as the physical and external force exerted or applied to an object.
Relation Between Pressure and Velocity
Ques. How do you find velocity from pressure? (1 Mark)
Ans.The static pressure (p) in the flow plus one half of the density (r) times the velocity (V) squared is equal to a constant throughout the flow, which we call the total pressure (pt) of the flow.
Ques. When do pressure and velocity decrease simultaneously? (2 Marks)
Ans. Pressure and Velocity can decrease simultaneously in case of liquids. Example: In a jar filled with water, if you make a hole somewhere near the bottom of the jar, the water will flow out through the hole at a certain velocity. As the water level in the jar decreases, velocity of the liquid coming out also decreases.
Ques. How do temperature and pressure affect the velocity of sound? (2 Marks)
Ans. As molecules vibrate faster, and heat increases, sound travels faster. However, speed of sound can also get affected by humidity and air pressure. The formula for speed of sound with respect to temperature is: v = 331 + 0.6*T where T is temperature.
Bernoulli’s Formula for Relation Between Pressure and Velocity
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Bernoulli's equation is the formulation of the energy conservation principle for fluid systems. In fluid mechanics, it is one of the most essential and useful equations. It establishes a relationship between pressure and velocity in an incompressible inviscid flow.
p1 + ½\(\rho\)v12 + \(\rho\)gh1 = p2 + ½\(\rho\)v22 + \(\rho\)gh2
Important Notes:
- Bernoulli's equation defines the qualitative behavior of a flowing fluid, which is sometimes referred to as Bernoulli's effect.
- In areas where the flow velocity is increased, this effect causes a drop in fluid pressure.
- The reduction of pressure in a flow route constriction may appear paradoxical, but it becomes less so when the pressure is considered to be energy density.
- Kinetic energy must grow at the expense of pressure energy in the high-velocity flow through the constriction. Kinetic energy per unit volume is the dimension of terms in the equation.
Bernoulli’s Theorem Video Explanation
Also Read: Quantum Physics
Laplace Correction for Newtonian Formula
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According to Laplace, sound wave propagation in air or gas is an adiabatic process, not an isothermal process as Newton claimed. As a result of the low thermal conductivity of air and the quick movement of compression and rarefaction in the air, heat does not flow out of or into the system, and the adiabatic gas equation is used to describe the change in volume and pressure of air.
PVr = constant
Through the Laplace Correction for the Newtonian formula the relation between pressure and velocity can be described as:
\(v = \sqrt{\frac{(\Upsilon P)}{\rho}}\)
Here,
- v refers to the velocity of sound waves in m/s
- p refers to the pressure present in the propagating medium in N/m²
- \(\rho\) refers to the density present in the propagating medium in kg/m³
- \(\Upsilon\) represents the adiabatic constant
Things to Remember
- In physics, velocity is defined as a vector measurement of motion's direction and rate.
- The physical force exerted on an object is known as pressure. The force applied per unit area is perpendicular to the surface of the objects.
- The relationship between pressure and velocity is inverse. When pressure rises, velocity.
- One thing that both macroscopic factors have in common when comparing pressure velocity relationships is that they both govern a wide range of natural occurrences.
- The sum of all kinds of energy in a fluid along a streamline is the same at all points on that streamline in a constant flow. The sum of kinetic energy, potential energy, and internal energy must remain constant for this to happen.
Previous Year Questions
- A ball whose density is 0.4×103kg/m3 falls into water from a height of 9cm… [BITSAT 2007]
- A boat with scrap iron in it is floating in a small tank of water… [JIPMER 1998]
- The cylindrical tube of a spray pump has radius R… [NEET 2015]
- Water rises to a height h in capillary tube… [NEET 2015]
- A certain number of spherical drops of a liquid of radius… [NEET 2014]
- A fluid is in streamline flow across a horizontal pipe of variable area of cross… [NEET 2013]
- A small sphere of radius ′r′ falls from rest in a viscous liquid… [NEET 2018]
- A rectangular film of liquid is extended from… [NEET 2016]
- A small hole of area of cross-section 2mm2 is present near the bottom of a fully… [NEET 2019]
- A soap bubble, having radius of 1mm, is blown from a detergent solution having… [NEET 2019]
- A liquid is filled upto a height of 20cm in a cylindrical vessel… [KEAM]
- The force acting on a window of area 50cm×50cm of a submarine at a depth… [KEAM]
- A small spherical ball falling through a viscous medium of negligible density… [KEAM]
- A spherical ball of diameter 1cm and density… [KEAM]
- Ice pieces are floating in a beaker A containing water and also in a beaker… [KEAM]
Sample Questions
Ques. What is the principle of conservation of energy? (3 marks)
Ans. The principle of conservation of energy states that during a steady flow, the sum of all forms of energy in a fluid along a streamlined flow is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy, and internal energy remains constant. As a result, an increase in the fluid's speed – meaning an increase in its kinetic energy (dynamic pressure) – is accompanied by a decrease in its potential energy (including the static pressure) and internal energy. Because the energy per unit volume in a reservoir is the same everywhere, the sum of all kinds of energy on all streamlines is the same if the fluid is flowing out of it.
Ques. Define the term ‘Pressure’? (3 marks)
Ans. The force exerted per unit area on the boundaries of a substance is measured as pressure. In the SI system, the Newton per square meter, or pascal, is the standard unit for pressure (Pa).
P = F/A
where
Pressure is P
Force is F
Area is A
The pressure exerted by a system on its surroundings is caused by the forces originating from all of these encounters. In a closed system, pressure is a constant intensive variable. It is only applicable to liquid or gaseous systems.
Ques. Define the term ‘Velocity’? (3 marks)
Ans. The velocity of an object is the rate at which its displacement changes over time in a specific direction.
Velocity = Displacement / Time taken
The definition of velocity for an object is the rate at which the object's position changes in relation to a frame of reference and time. It may sound difficult, but velocity simply refers to the rate at which something moves in a given direction. It has the SI unit of meter per second (ms-1).
Ques. What is Bernoulli’s Formula for Relation Between Pressure and Velocity? (3 marks)
Ans. Bernoulli's equation, named after its discoverer, Swiss physicist Daniel Bernoulli (1700–1782), quantifies the relationship between pressure and velocity in fluids. According to Bernoulli's equation, the following sum is constant for an incompressible, frictionless fluid:
p + ½ \(\rho\)v2 + \(\rho\)g h = constant
P is the absolute pressure, the fluid density, v is the fluid velocity, h is the height above some reference point, and g is the gravity acceleration.
p1 + ½\(\rho\) v12 + \(\rho\) g h1 = p2 + ½ \(\rho\) v22 +\(\rho\) g h2
Ques. What is Laplace Correction for Newtonian Formula? (3 marks)
Ans. Newton has extended Boyle's law to pressure changes and volume changes, based on Laplace's assumption that isothermal conditions predominate as sound travels through the air. There is a minimal increase in temperature in a compression region and a marginal decrease in temperature in a rarefaction region. According to Laplace, because these pressure changes occur quickly and the air is a poor conductor of heat, temperature equalization between the various zones was improbable. He believed that temperature changes occur under adiabatic conditions, which means that no heat enters or exits the gas from the outside. The heat generated in the compressed layers is completely confined to these layers and does not have time to diffuse across the entire gas body. Similarly, the cold created in rarefied layers cannot be compensated by heat transfer from other layers inside it.
Ques. In fluid dynamics, what is the connection between velocity, pressure, and area? Will the velocity rise or drop as the area grows? (5 marks)
Ans. The area of a cross-section of the body through which a fluid is flowing is inversely related to velocity and pressure.
Let us assume, we have two cross-sections A and B of different areas, A1 and A2 respectively. Suppose the velocities at these two different points be v1 and v2 respectively. Assuming the fluid is incompressible, the volume of the fluid that is flowing through any point of the pipe in a given duration is the same. This phenomenon is called the 'continuity equation'.
A1v1=A2v2
In simple words, the velocity is higher where the area is smaller,
Pressure and velocity are inversely related, according to Bernoulli's principle (which is really just a formulation of the conservation of energy). The pressure reduces as the velocity increases in a scenario where a fluid flows into a narrower cross-section. In fact, it is the pressure differential that keeps the motion toward the smaller cross-section stable.
Take two equal-height points as an example (gravitational potential). As can be observed from the above, the lower the pressure, the higher the velocity.
Ques. Why is pressure inversely proportional to velocity? (2 marks)
Ans.This relation is due to the law of conservation of energy at the molecular level
As air moves with high velocity, all air particles collide with each other and move apart from each other. Due to this, the same number of air particles now takes more space or in other words, volume taken by the same amount of air particles now increases.
As we know,
PV=constant(at constant temperature)
So, when volume increases, pressure decreases.
Also Read:
| Related Links | ||
|---|---|---|
| Latent Heat | Heat Transfer | Specific Heat Capacity |
| Calorimetry | Density of Air | Relation between Viscosity and Density |
| Blackbody Radiation | Properties of Matter | Thermal Energy |
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