Fluid mechanics - pump in a horizontal pipe connecting two pipes

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SUMMARY

The discussion focuses on calculating the head loss in a horizontal pipe system using Bernoulli's equation. The initial calculation yields a head loss of 10.2 meters without considering pressure loss at the orifice, where the pressure differential (dp) is calculated as 100,000 Pa. After accounting for the pressure loss due to the orifice, the revised head loss is 10.03 meters. However, the user is seeking clarification on why the expected head loss is significantly higher than the calculated 1,613 Pa, indicating a potential oversight in the pressure loss estimation.

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Homework Statement
Hey guys, my problem is in the linked task the first letter a). I tried to calculate this problem since 2 hours and dont get on the solution. Please excuse my english, its not my native language.
Relevant Equations
g*h1+p1/rho+(v1^2)/2 = g*h2+p2/rho + v2^2/2 + dpl
dpl = Pressure loss

dpl = 1/2 * rho * v1^2 * loss coefficient
So when the velocity of v1 and v2 is 0 (because the tanks are much bigger), the bernoulli equation to dh is dh = (dp-dpl)/(rho*g)

with dp = Phyd / V = 1000W / 0.01m³/s = 10^5 Pa and rho = 1000 kg/m³

So I am getting first without the pressure loss on the orifice dh = 10^5 Pa / (1000 kg/m³ * 9,81 m/s²) = 10.2m

So the loss coefficient for a standard orifice and for D2/D1 = 0.6 is 2 (according of the supplement what our prof gave us)

v1 = V / (r2²*pi) = 1.27 m/s

dpl = 1/2 * 1000 kg/m³ * (1.27 m/s)² * 2 = 1613 Pa

Now I am gettin dh with the pressure loss

dh = (10^5 Pa - 1613 Pa) / (1000 kg/m³ * 9,81 m/s² ) = 10.03m

Still don't get to the 6.8m. And I don't know what up, so the pressure loss should be much much bigger than these 1613 Pa.

Im very thankfull for every help.
 

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Your equations are very hard to read. Please use LaTex.
 

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