The pipe must drop in height by 13.101 m in order to achieve this pressure.
Bernoulli stated that at whatever point along the fluid flow, the total amount of pressure, kinetic energy and potential energy per unit volume is the same.
P + 1/2 ρv² + ρ* g* h = constant
Given that, v = 1 m/s
P₁ = 101300 Pa
P₂ = 202600 Pa
ρ ethanol = 789 kg/m³
g = 9.8 m/s²
Now, let us write the bernoulli equation,
ρ*g*h₁ + P₁ = ρ*g*h₂ + P₂
P₁ - P₂ = ρ*g*h₂ - ρ*g*h₁
( h₂ - h₁) = (P₁ - P₂)/ρ*g
Δh = (P₁ - P₂)/ρ*g
Δh = -101300 / ( 789 * 9.8) = -13.101 m
Minus sign indicates that height must be reduced.
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