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Fluid is a substance that can flow. And, dynamics refers to the study of motion under the effect of forces. So, fluid dynamics is concerned with the motion of fluid under the action of forces.

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It tells us a relationship between the speed of flow and the cross-sectional area of the channel or tube.

= constant

The discharge (Q) will remain constant throughout the tube. A decrease in the cross-sectional area (A) would increase the speed of flow (v).

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In an ideal fluid, applying the principle of conservation of mechanical energy leads to Bernoulli's Equation.

= constant

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 .

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**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,

So,

**Final answer: **The velocity at the outlet would be .

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**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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