It tells us a relationship between the speed of flow and the cross-sectional area of the channel or tube.
The discharge (Q) will remain constant throughout the tube. A decrease in the cross-sectional area (A) would increase the speed of flow (v).
In an ideal fluid, applying the principle of conservation of mechanical energy leads to Bernoulli's Equation.
At every point on the flow tube, the sum of pressure, kinetic energy density, and potential energy density would remain constant.
Question 1: A uniform cylindrical tube has a cross-sectional area (A) of . If, the discharge (Q) is . Calculate the velocity (v) of the fluid.
Explanation: Using the equation of continuity:
Final answer: The velocity of the fluid would be .
Question 2: The inlet cross-sectional area of a tube is , and the outlet cross-sectional area is . If, the fluid entering on the tube with a velocity of . Calculate the velocity of the fluid at the outlet.
Explanation: The discharge at the inlet and at the outlet would remain the same. Rewrite the equation of continuity to get the velocity at the outlet.
Given: , . And,
Final answer: The velocity at the outlet would be .
Question 3: A cylindrical water tank has a height of . Initially, the tank was completely filled with water. A small hole with a cross-section area of is made at the side of the tank at the bottom. Find the speed of water from the hole at the bottom level.
Explanation: We will apply Bernoulli's Equation between the top of the tank and the bottom of the tank. Also, there is no external pressure, and .
Final answer: The speed at the bottom side would be .
Fluid dynamics stands for the flow of liquids or refers to that branch of applied science that deals with the movement of gases and liquids.
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The basic principle of fluid dynamics is the equation of continuity.
It tells us a relationship between the speed of flow v, and the cross-sectional area A, and the discharge Q, of the channel or tube.
Fluid dynamics is used to study the motion of the fluid under the pressure. Some real-life technological applications of fluid dynamics can be seen in turbines, wind turbines, air conditioning, oil and gas pipelines.
Fluid dynamics is considered an important topic in fluid mechanics. We study the behavior of liquid and gas under the action of pressure.
Since liquid and gas has not a definite shape, when they flow, it becomes difficult to represent the flow using equations. Hence, some assumption needs to be made.
If someone is good at Differential Equations, Multivariable Calculus, Tensor Analysis, I think they will not consider fluid dynamics so hard.
I think this depends upon how much you understand the mathematical equations used in fluid dynamics.
We study laminar flow at the beginning of fluid dynamics, and we assume the fluid is ideal. So, the mathematical equations used for them are comparatively easy.
Then we study the turbines. This part of fluid dynamics involves different equations for different turbines. So, here we have more equations.
When we study turbulent flow, unsteady flow, discretization, etc. You may see some advanced mathematical equations. This part of fluid dynamics is comparatively hard.
Under fluid mechanics, we study the behavior of fluid and force on them. Fluid can be at rest or at motion.
However, under fluid dynamics, we study the fluid flow under pressure. In this section, fluid will be in motion. This is a sub-part of fluid mechanics.