A hydrodynamics is an area of Physics, specifically classical mechanics, which comprises the fluids dynamic ideals, those that are moving. In it we mainly study the mass flow rate, the volumetric flow rate of fluids, the continuity equation and Bernoulli's principle.
Read too: Aerodynamics — the branch of Physics that studies the interaction of gases with air
Summary on hydrodynamics
- Hydrodynamics is an area of classical mechanics that studies ideal fluids in motion.
- Its main concepts are: mass flow, volumetric flow, continuity equation, and Bernoulli's principle.
- Based on the volumetric flow rate, we know the amount of volume of a fluid that passes through a straight section during a time interval.
- Based on the mass flow rate, we know the amount of mass of a fluid that passes through a straight section during a period of time.
- Based on the continuity equation, we observe the influence of the cross-sectional area on the flow speed of an ideal fluid.
- Based on Bernoulli's principle, we observe the relationship between the speed and pressure of an ideal fluid.
- Hydrodynamics is applied in the construction of airplanes, cars, houses, buildings, helmets, taps, plumbing, vaporizers, Pitot tubes, and Venturi tubes.
- While hydrodynamics is an area of Physics that studies ideal fluids in motion, hydrostatics is an area of Physics that investigates static fluids.
What is hydrodynamics?
The hydrodynamics is an area of Physics, specifically of classical mechanics, which studies ideal fluids (liquids and gases) in motion. An ideal fluid is one that has: laminar flow, in which the intensity, direction and direction of its speed at a fixed point do not change over time; incompressible flow, in which its specific mass is constant; non-viscous flow, presenting low flow resistance; and irrotational flow, not rotating around an axis that crosses its center of mass.
Hydrodynamics concepts
The main concepts studied in hydrodynamics are mass flow, volumetric flow, continuity equation and Bernoulli's principle:
- Volumetric flow: is a physical quantity that can be defined as the amount of volume of a fluid that crosses a straight section during an interval of time. It is measured in cubic meters per second [m3/s] .
- Mass flow: is a physical quantity that can be defined as the amount of mass of a fluid that crosses a straight section during an interval of time. It is measured in [kg/s] .
- Continuity equation: deals with the relationship between speed and the cross-sectional area, in which the flow speed of an ideal fluid increases as the cross-sectional area through which it flows decreases. This equation is exemplified by the image below:
- Bernoulli's principle: deals with the relationship between the speed and pressure of an ideal fluid, in which if the speed of a fluid becomes larger as it flows through a flow line, then the pressure of the fluid becomes lower and vice versa. This principle is exemplified by the image below:
Hydrodynamic formulas
→ Volumetric flow formula
\(R_v=A\cdot v\)
- Rv → volumetric flow of the fluid, measured in [m3/s] .
- A → flow section area, measured in square meters [m2].
- v → average speed of the section, measured in meters per second [m/s].
→ Mass flow formula
When the density of the fluid is the same at all points, we can find the mass flow rate:
\(R_m=\rho\cdot A\cdot v\)
- Rm → mass flow rate of the fluid, measured in [kg/s] .
- ρ → fluid density, measured in [kg/m3].
- A → flow section area, measured in square meters [m2].
- v → average speed of the section, measured in meters per second [m/s].
→ Continuity equation
\(A_1\cdot v_1=A_2\cdot v_2\)
- A1 → area of flow section 1, measured in square meters [m2].
- v1 → flow speed in area 1, measured in meters per second [m/s].
- A2 → area of flow section 2, measured in square meters [m2].
- v2 → flow speed in area 2, measured in meters per second [m/s].
→ Bernoulli equation
\(p_1+\frac{\rho\cdot v_1^2}{2}+\rho\cdot g\cdot y_1=p_2+\frac{\rho\cdot v_2^2}{2}+\rho\cdot g\cdot y_2\)
- P1 → fluid pressure at point 1, measured in Pascals [Shovel].
- P2 → fluid pressure at point 2, measured in Pascals [Shovel].
- v1 → fluid velocity at point 1, measured in meters per second [m/s].
- v2 → fluid speed at point 2, measured in meters per second [m/s].
- y1 → fluid height at point 1, measured in meters [m].
- y2 → fluid height at point 2, measured in meters [m].
- ρ → fluid density, measured in [kg/m3 ].
- g → acceleration of gravity, measures approximately 9,8 m/s2 .
Hydrodynamics in everyday life
The concepts studied in hydrodynamics are widely used in build planes, cars, houses, buildings, helmets and more.
The study of the flow allows us to make the measuring water flow in homes and industrial treatment plants, in addition to assessments of the quantities of industrial gases and fuels.
The study of Bernoulli's principle has Wide use in Physics and engineering, mainly in the creation of vaporizers and Pitot tubes, to measure the speed of air flow; and in the creation of Venturi tubes, to measure the flow speed of a liquid inside a pipe.
Based on the study of the continuity equation, it is possible to have understanding the working principle of faucets and why, when you put your finger in the water outlet of a hose, the speed of the water increases.
Differences between hydrodynamics and hydrostatics
Hydrodynamics and hydrostatics are areas of physics responsible for studying fluids:
- Hydrodynamics: area of Physics that studies dynamic fluids in movement. In it we study the concepts of volumetric flow, mass flow, continuity equation and Bernoulli's principle.
- Hydrostatic: area of Physics that studies static fluids, at rest. In it we study the concepts of specific mass, pressure, Stevin's principle and its applications, and Archimedes' theorem.
See too:Kinematics — the area of Physics that studies the movement of bodies without taking into account the origin of the movement
Solved exercises on hydrodynamics
Question 1
(Enem) To install an air conditioning unit, it is suggested that it be placed on the upper part of the room wall, as the Most fluids (liquids and gases), when heated, undergo expansion, having their density reduced and suffering a displacement ascending. In turn, when they are cooled, they become denser and undergo a downward displacement.
The suggestion presented in the text minimizes energy consumption, because
A) reduces the humidity of the air inside the room.
B) increases the rate of thermal conduction out of the room.
C) makes it easier for water to drain out of the room.
D) facilitates the circulation of cold and hot air currents within the room.
E) reduces the rate of heat emission from the device into the room.
Resolution:
Alternative D
The suggestion presented in the text reduces electrical energy consumption, as cold air rises and hot air descends, facilitating the circulation of cold and hot air currents within the room.
Question 2
(Unichristus) A cistern with a capacity of 8000 liters is completely filled with water. All the water from this cistern will be pumped into a water tanker with a capacity of 8000 liters at a constant flow rate of 200 liters/minute.
The total time required to remove all the water from the cistern to the tanker truck will be
A) 50 minutes.
B) 40 minutes.
C) 30 minutes.
D) 20 minutes.
E) 10 minutes.
Resolution:
Alternative B
We will calculate the total time required using the volumetric flow formula:
\(R_v=A\cdot v\)
\(R_v=A\cdot\frac{x}{t}\)
\(R_v=\frac{V}{t}\)
\(200=\frac{8000}{t}\)
\(t=\frac{8000}{200}\)
\(t=40\ min\)
Sources
NUSSENZVEIG, Herch Moysés. Basic physics course: Fluids, Oscillations and Waves, Heat (vol. 2). 5 ed. São Paulo: Editora Blucher, 2015.
HALLIDAY, David; RESNICK, Robert; WALKER, Jearl. Fundamentals of Physics: Gravitation, Waves and Thermodynamics (vol. 2) 8. ed. Rio de Janeiro, RJ: LTC, 2009.