# How Does Pipe Area Change Affect Fluid Velocity and Pressure?

• Brabs23
In summary, using the Bernoulli equation and the continuity equation, the inlet velocity and mass flow rate of water through the circular pipe can be calculated based on the given information. The pipe has a fall of 4m and its area decreases to one quarter at the exit. The pressure at the inlet is 20kN/m^2 above atmospheric and at the exit, where the velocity is 15m/s, the pressure is atmospheric.
Brabs23
A circular pipe has a fall of 4m and narrows so that, at exit, its area is one quarter that at inlet. The pressure at inlet is 20kN/m^2 above atmospheric and at exit, where the velocity is 15m/s, the pressure is atmospheric.

Calculate the inlet velocity and mass flow rate of water through the pipe per unit cross-sectional area at inlet.

Relevant Equations: Bernoullis

I've got this so far (if it is correct!):

4 + (20 x 10³)/10³ x g + V²/2g = 15²/2g + h

I'm not sure how to use the area values given to find out the velocity .. I presume I need to use Q = AV?

Continuity equation:
$$A_{1}v_{1} = A_{2}v_{2}$$

And Bernoulli is all you need.

## 1. What is simple fluid mechanics?

Simple fluid mechanics is the study of how fluids, such as liquids and gases, behave and interact with their surroundings. It involves understanding the fundamental principles and equations that govern the motion and properties of fluids.

## 2. What are some examples of simple fluid mechanics in everyday life?

Simple fluid mechanics can be observed in various everyday situations, such as the flow of water through a faucet, the movement of air in a room, or the flight of a paper airplane. It is also essential in industries like aviation, automotive, and oil and gas.

## 3. How is simple fluid mechanics different from complex fluid mechanics?

Simple fluid mechanics deals with idealized scenarios where fluids are considered to be non-viscous and incompressible. In contrast, complex fluid mechanics takes into account the effects of viscosity, compressibility, and turbulence on fluid behavior. It also involves more advanced mathematical techniques and computational methods.

## 4. What are the main principles of simple fluid mechanics?

The main principles of simple fluid mechanics include conservation of mass, conservation of momentum, and conservation of energy. These principles are expressed through equations such as Bernoulli's equation, Euler's equation, and Navier-Stokes equations.

## 5. How is simple fluid mechanics used in engineering and research?

Simple fluid mechanics is crucial in the design and analysis of various engineering systems, such as pumps, turbines, and airfoils. It is also used in research to understand and predict the behavior of fluids in different environments, such as in oceans, rivers, and the Earth's atmosphere.

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