MHB Bernoulli's Equation: Solving Complex Problems Easily

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Bernoulli's equation is presented as a key tool for solving fluid dynamics problems, specifically in the context of pressure and velocity changes in a fluid. The equation is detailed, highlighting the relationship between kinetic energy, potential energy, and pressure in a fluid system. A specific scenario is discussed where one point is a stagnation point, leading to the conclusion that the velocity at that point is zero. The conversation encourages the user to fill in the variables to solve for the initial velocity, prompting further engagement on the problem. Overall, the discussion emphasizes the application of Bernoulli's equation to simplify complex fluid dynamics questions.
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Hi All,

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

Thanks in advance.
 

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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.

Thanks in advance.

Hi jc91, welcome to MHB! ;)

Let's start with Bernoulli's equation:
$$\frac 12 \rho v_1^2 + \rho g z_1 + p_1 = \frac 12 \rho v_2^2 + \rho g z_2 + p_2$$
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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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