# Fluids bernoulli's equation problem

In summary, the conversation is about two horizontal tubes of different diameters and the pressure difference between them. The question is which tube has a higher pressure flow and which has a higher speed flow. The formula P2=p1+ (1/2)density(rho)(v1^2-v2^2) is mentioned, but the problem is how to solve without knowing the velocity. It is stated that pressure is greater in the bigger area with less fluid speed, while the greater fluid speed has the least pressure. Without worrying about numbers, it is asked to determine the speeds in the tubes as functions of the pressures in each part. This would allow for solving for all unknowns, including the desired velocity.
Water flows throgh a horizontal tube of diameter 2.8cm that is joined to a second horizontal tube of diameter 1.6cm. the pressure difference between the tubes is 7.5kPa. which tube has the higher pressure flow? which tube has the higher speed flow? find the speed of flow in the first tube.

P2=p1+ (1/2)density(rho)(v1^2-v2^2)

how can i solve without a velocity 1 or 2?

Without worrying about numbers (quantitative parts) -- can you first answer the qualitative parts?

pressure is greater in the bigger area with less fluid speed. the greater fluid speed has the least pressure.

Okay -- now say you KNOW the pressure in each part -- just call them dummy variables say P_b and P_s for the big and small diameter tubes. Can you then individually know the speeds in the tubes as functions of P_b and P_s? then you know the difference between P_b and P_s. Try setting up those... Then you might have as many equations as unknowns ands be able to solve for all your unknowns, including the velocity you want.

## 1. What is Bernoulli's equation and how is it used in fluid mechanics?

Bernoulli's equation is an important tool in fluid mechanics that relates the pressure, velocity, and height of a fluid in a closed system. It is based on the principle of conservation of energy and can be used to calculate various properties of a fluid, such as its flow rate or pressure at different points.

## 2. How is Bernoulli's equation derived?

Bernoulli's equation is derived from the principles of conservation of mass and energy, along with the assumption of a non-viscous, incompressible fluid. It can also be derived using the Euler equations, which describe the motion of a fluid in terms of its pressure, density, and velocity.

## 3. What are the limitations of Bernoulli's equation?

Bernoulli's equation is only applicable to ideal fluids, which do not exist in real life. It also assumes that the flow is steady, incompressible, and has a constant density. Additionally, it does not account for the effects of viscosity and turbulence in a fluid.

## 4. How is Bernoulli's equation used to solve problems?

To solve a problem using Bernoulli's equation, you must first identify the known and unknown variables, such as pressure, velocity, and height. Then, you can use the equation to set up a system of equations and solve for the unknown variables using algebraic manipulation. It is also common to use Bernoulli's equation in conjunction with other equations, such as the continuity equation, to fully solve a fluid mechanics problem.

## 5. Can Bernoulli's equation be applied to any type of fluid?

No, Bernoulli's equation can only be applied to ideal fluids, which do not exist in real life. Real fluids have varying densities, viscosities, and compressibility, which make it difficult to use Bernoulli's equation accurately. However, it can still provide a good approximation for some real-life fluid problems.

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