# Bernoulli's Equation: Solving Complex Problems Easily

• MHB
• jc911
In summary, the conversation is about Bernoulli's equation and how to solve for $v_1$ using the given information. The question also asks for clarification on the blue scribble and its meaning.
jc911
Hi All,

Could anyone advise on how to answer below question (attached). I am struggling big time on this.

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jc91 said:
Hi All,

Could anyone advise on how to answer below question (attached). I am struggling big time on this.

Hi jc91, welcome to MHB! ;)

$$\frac 12 \rho v_1^2 + \rho g z_1 + p_1 = \frac 12 \rho v_2^2 + \rho g z_2 + p_2$$
Or do you perhaps have a different version of it?

Since (2) is a stagnation point, we have $v_2=0$.
The pressure is identified by the column of water above it: it's the weight per surface area.
And additionally we have the standard pressure of air ($p_0$).
So for instance $p_1 = p_0 + \rho g (h_1 + h_2)$.

How far do you get filling in the other variables and solving for $v_1$?

Question for jc91: what is underneath the blue scribble?

## 1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between pressure, velocity, and height in a fluid flow. It states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid remains constant along a streamline.

## 2. How is Bernoulli's equation used in solving complex problems?

Bernoulli's equation can be used to solve a wide range of problems in fluid dynamics, including problems involving flow rate, pressure changes, and velocity changes. It can also be used to analyze the behavior of fluids in various systems, such as pipes, pumps, and airplanes.

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

The assumptions of Bernoulli's equation are that the fluid is incompressible, non-viscous, and steady-state. It also assumes that the flow is along a streamline, and that there is no external work being done on the fluid.

## 4. Can Bernoulli's equation be applied to any fluid?

Bernoulli's equation can be applied to any fluid, as long as the assumptions hold true. However, it may not accurately describe certain fluids, such as gases or highly viscous fluids, which require more complex equations to model their behavior.

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

Bernoulli's equation can be derived from the principles of conservation of mass and energy, along with the fluid's equation of motion. It can also be derived from the Navier-Stokes equations, which describe the motion of fluids.

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