I wanted the solution of H C Verma, Fluid Mechanics. Question No is 15

To tackle question number 15 from H.C. Verma's "Fluid Mechanics," let's first clarify the context of the problem. Typically, questions in this section involve concepts like fluid statics, dynamics, or the principles of buoyancy and pressure. While I can't provide the exact text of the question, I can guide you through a common type of problem you might encounter in this chapter and help you understand how to approach it.

Understanding Fluid Pressure

In fluid mechanics, pressure is a fundamental concept. It is defined as the force exerted per unit area. The formula for pressure (P) in a fluid at a certain depth (h) is given by:

P = ρgh

Where:

• P = pressure at depth
• ρ = density of the fluid
• g = acceleration due to gravity (approximately 9.81 m/s²)
• h = depth of the fluid column

Applying the Concept

Let’s say the problem involves calculating the pressure at a certain depth in a fluid. For example, if you have a tank filled with water and you need to find the pressure at a depth of 5 meters, you would follow these steps:

1. Identify the density of the fluid. For water, ρ is approximately 1000 kg/m³.
2. Use the formula to calculate pressure:

P = ρgh

P = 1000 kg/m³ × 9.81 m/s² × 5 m

P = 49050 Pa

This means the pressure at a depth of 5 meters in water is 49,050 Pascals (Pa).

Exploring Buoyancy

Another common theme in fluid mechanics is buoyancy, which is described by Archimedes' principle. This principle states that an object submerged in a fluid experiences an upward force equal to the weight of the fluid displaced by the object. If the question involves buoyancy, you might need to calculate the buoyant force acting on an object.

To find the buoyant force (F_b), use the formula:

F_b = ρ_fluid × V_displaced × g

Where:

• F_b = buoyant force
• ρ_fluid = density of the fluid
• V_displaced = volume of fluid displaced by the object
• g = acceleration due to gravity

Example of Buoyant Force Calculation

Imagine you have a cube with a volume of 0.1 m³ submerged in water. To find the buoyant force:

1. Calculate the weight of the water displaced:

F_b = 1000 kg/m³ × 0.1 m³ × 9.81 m/s²

F_b = 981 N

This indicates that the buoyant force acting on the cube is 981 Newtons.

Final Thoughts

By understanding these fundamental principles of fluid mechanics, you can approach various problems with confidence. Whether it’s calculating pressure at a certain depth or determining the buoyant force on an object, the key is to apply the relevant formulas correctly and understand the physical concepts behind them. If you have the specific details of question 15, feel free to share, and we can dive deeper into that particular problem together!