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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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