Dynamic fluids: types, characteristics, Bernoulli's equation, Toricelli's theorem, formulas and examples of problems

Dynamic Fluids: Types, Features, Bernoulli's Equation, Toricelli's Theorem, Formulas and Examples of Problems – What is a dynamic fluid and its types? On this occasion, Se regarding the knowledge.co.id will discuss it and of course about other things that also cover it. Let's look at the discussion together in the article below to better understand it.

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Dynamic fluids: types, characteristics, Bernoulli's equation, Toricelli's theorem, formulas and examples of problems

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Fluid is a substance that can flow. The word fluid includes car, water and gas because these two substances can flow, whereas rock and hard objects or all solid substances are not classified as fluids because they cannot flow.

All liquids can be grouped into fluids because they can flow from one place to another. Apart from liquids, gases are also fluids. Gases can also flow from one place to another. Blowing wind is an example of air moving from one place to another.

Fluid is one important aspect in everyday life. Every day humans breathe it, drink it, float or sink in it. Every day airplanes fly through it and ships float above it.

Likewise a submarine can float or float in it. The water we drink and the air we breathe also circulates in the human body all the time, although we often don't realize it.

Dynamic fluids are fluids (can be liquids, gases) that move. For convenience in studying, the fluid here is considered steady (has a constant velocity with respect to time), incompressible (not changing volume), not viscous, not turbulent (not experiencing rounds).

Hydrodynamics is the science that studies fluids in motion. Before studying moving fluids, it is necessary to know the ideal fluid and the types of fluid flow.

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Ideal Fluid

An ideal fluid is a fluid that is incompressible, moves without experiencing friction, and has a stationary flow:

• The flow is steady, that is, the velocity of each fluid particle at a certain point is constant, both in size and direction. Steady flow occurs in slow flow.
• The flow is irrational, meaning that at every point the fluid particle has no angular momentum with respect to that point. The flow follows the current line (streamline).
• Incompressible (incompressible), meaning that the fluid does not experience a change in volume (density) due to pressure.
• It is not viscous, meaning that it does not experience friction either with the surrounding fluid layers or with the walls through which it passes. Viscosity in fluid flow is related to viscosity.

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Fluid Flow Type

There are several types of fluid flow. The path taken by a fluid in motion is called the flow line. Here are some types of fluid flow, namely as follows:

• Straight or laminar flow is smooth fluid flow. The adjacent layers glide smoothly over each other. In this flow the fluid particles follow a smooth path and these paths do not cross each other. Laminar flow is found in water flowing through pipes or hoses.
• Turbulent flow is flow that is characterized by the presence of erratic circles and resembles a vortex. Turbulent flow is often found in rivers and ditches.

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Dynamic Fluid Characteristics

The general characteristics of fluid dynamics are as follows:

• fluid is considered incompatible
• fluid is considered to move without friction, even though there is movement of the material (it has no viscosity)
  Fluid flow is stationary flow, that is, the speed and direction of motion of the pulid particles passing through a certain point are always fixed
• independent of time (steady), meaning that the velocity is constant at a certain point, and forms a laminar (layered) flow

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Dynamic Fluid Formulas

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  debit

Debit is the amount of fluid volume flowing in unit time (generally per second)

Where :

Q = flow rate (m³/s)

A = cross-sectional area (m²)

V = fluid flow rate (m/s)

Fluid flow is often expressed in terms of flow rate

Where :

Q = flow rate (m³/s)

V = volume (m³)

t = time interval (s)

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  Toricelli's theorem

Toricelli's theorem is a phenomenon of water gushing out of a water tank hole.

The magnitude of the kinetic energy of the water that spurts out of the water tank hole is equal to the magnitude of the potential energy.

Therefore, the speed of the water spraying at the hole is the same as water falling freely from the water level limit.

Because the greater the difference between the height of the hole and the water level limit, the faster the water spray will be.

X= 2√(hH)
t = √(2H/g)

Information :
v is the velocity of liquid leaving the hole
H is the distance where the liquid (soil) falls to the leak hole
X is the horizontal distance the liquid falls
t is the time it takes for the liquid to touch the ground
h is the distance from the liquid surface to the leak hole

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  Continuity Equation

The continuity equation is an equation that relates the fluid velocity in one place to another.

Before deriving a relationship, it is better to understand some fluid flow terms. The flow line can be interpreted as an ideal fluid flow path (soft flow).

The tangent is at a point on the line that gives the direction of velocity to the fluid flow.

Fluid flow lines do not intersect one another. The water tube is a collection of flow lines.

Q1 = Q2
A1v1 = A2v2

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  Bernoulli's equation

Bernoulli's law is a law that is based on the law of the conservation of energy and is experienced in fluid flow.

This law states that the amount of pressure (p), kinetic energy pressure per unit volume, & potential energy per unit volume, has the same value at every point along a current line.

P + 1/2 ρv2 + ρgh = Constant

P1 + 1/2 ρv12 + ρgh1 = P2 + 1/2 ρv22 + ρgh2

Information :
P is pressure (Pascal = Pa = N/m2)
ρ is the density of the fluid; liquid or gas (kg/m3)
g is the acceleration due to gravity (m/s2)

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Examples of Dynamic Fluid Problems

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Problem 1.

2012/2013 SMA Physics National Examination Questions SA 55 No.15

A large tub filled with water and there is a faucet like the picture. If g = 10 ms^-2, then the speed of the water spray from the faucet is...

A 3 ms^-1
B. 8 ms^-1
C. 9 ms^-1
D. 30 ms^-1
E. 900 ms^-1

Discussion
Is known :
Height (h) = 85 cm – 40 cm = 45 cm = 0.45 meters
Acceleration due to gravity (g) = 10 m/s²
Wanted: Speed ​​of water spray from the faucet (v)
Answer :

Torricelli's theorem states that the speed of a jet of water through a hole a distance h from the surface of the water is equal to the speed of free fall of water from a height h.
The speed of the water jet is calculated using the free fall motion formula v_t² = 2 g h
v_t² = 2 g h = 2(10)(0.45) = 9
v_t = √9 = 3 m/s
The correct answer is A.

Problem 2.

Pipes for channeling water attached to a wall of the house as shown in the following picture! The ratio of the cross-sectional area of ​​a large pipe and a small pipe is 4: 1.
The position of the large pipe is 5 m above the ground and the small pipe is 1 m above the ground. The velocity of the water flow in the large pipe is 36 km/hour with a pressure of 9.1 x 10⁵ Pa. Define:

a) The velocity of the water in the small pipe

b) Difference in pressure in the two pipes
c) Pressure in small pipe
(ρ_water = 1000 kg/m³)

Discussion
Known: h₁ = 5 m; h₂ = 1m; v₁ = 36 km/h = 10 m/s; P₁ = 9.1 x 10⁵ Pa; A₁: A₂ = 4: 1

a) The velocity of the water in the small pipe
Continuity Equation :
A₁v₁ = A₂v₂
(4)(10) = (1) (v₂)
v₂ = 40m/s

b) Difference in pressure in the two pipes
From Bernoulli's Equation:
P₁ + ¹/₂ ρv₁² + ρgh₁ = P₂ + ¹/₂ ρv₂² + ρgh₂
P₁ − P₂ = ¹/₂ ρ(v₂² − v₁²) + ρg (h₂ − h₁)
P₁ − P₂ = ¹/₂(1000)(40² − 10²) + (1000)(10)(1 − 5)
P₁ − P₂ = (500)(1500) − 40000 = 750000 − 40000
P₁ − P₂ = 710000 Pa = 7.1 x 10⁵ Pac) Pressure in small pipe
P₁ − P₂ = 7.1 x 10⁵
9.1 x 10⁵ − P₂ = 7.1 x 10⁵
P₂ = 2.0 x 10⁵ Pa

Problem 3.

A reservoir filled with water and in the wall there is a hole (see picture). The speed of the water as it exits the hole is… (g = 10 ms^-2)

A 12 ms^-1
B. 10ms^-1
C. 6 ms^-1
D. 5 ms^-1
E. 2 ms^-1

Discussion
Is known :
Height (h) = 1.5 m – 0.25 m = 1.25 meters
Acceleration due to gravity (g) = 10 m/s²
Wanted: Speed ​​of water as it leaves the hole (v)
Answer :
v_t² = 2 g h = 2(10)(1,25) = 25
v_t = √25 = 5 m/s
The correct answer is D.

Problem 4.

A tank filled with water 1 meter high (g = 10 ms^-2) and on the wall there is a leak hole (see picture). The speed of the water coming out of the hole is...
A 1 ms^-1
B. 2 ms^-1
C. 4 ms^-1
D. 8 ms^-1
E. 10ms^-1
Discussion
Is known :
Height (h) = 1 m – 0.20 m = 0.8 meters
Acceleration due to gravity (g) = 10 m/s²
Wanted: Speed ​​of water as it leaves the hole (v)
Answer :
v_t² = 2 g h = 2(10)(0.8) = 16
v_t = √16 = 4 m/s
The correct answer is D.

Problem 5.

A pipe carries water with a discharge of 1M3 every second, and will be used to fill a dam measuring (100 X 100 X 10) M. Then calculate the time required to fill the Dam to the brim!.

Answer :

So the answer is the time needed for the dam to be full, namely 100,000 seconds.

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