Answer:

The pressure P1 at the entrance end of the pipe = 444,001.4 Pa = 4.382 atm

Explanation:

The Bernoulli’s principle is basically a law of conservation of energy, it theorizes that the sum of the energy due to pressure, kinetic energy and potential energy of a fluid is constant all through the points of the fluid motion.

Or that the losses due to pressure effects, kinetic effects and potential effects is equal to 0 all through the fluids motion.

It is given mathematically as

[(P₂ – P₁)/ρg] + [(v₂² – v₁²)/2g] + [z₂ – z₁] = 0

P₂ = Pressure at the exit = 1.3 atm = 1.3 × 101325 = 131,722.5 Pa

P₁ = Pressure at the entrance end = ?

ρ = density of the fluid = 1237 kg/m³

g = acceleration due to gravity = 9.8 m/s²

v₁ = velocity of the fluid at the entrance end = 1.84 m/s

v₂ = velocity of the fluid at the exit = ?

But we can obtain this using the continuity equation, the continuity equation stated mathematically is

ρ₁ A₁ v₁ = ρ₂A₂v₂

Since the density of the fluid is constant all through, the continuity equation becomes

A₁ v₁ = A₂ v₂

A₁ = cross sectional Area At the entrance end = (πd₁²/4)

A₂ = cross sectional Area At the exit = (πd₂²/4)

The continuity equation then further becomes

d₁² v₁ = d₂² v₂

0.18² × 1.84 = 0.05² × v₂

v₂ = 23.8464 m/s

z₂ = elevation of the exit end

z₁ = elevation of the entrance end

z₂ – z₁ = -3.08 m (minus sign because the exit end is lower than the entrance end)

[(P₂ – P₁)/ρg] + [(v₂² – v₁²)/2g] + [z₂ – z₁] = 0

Multiplying through by ρg, the Bernoulli equation becomes

[(P₂ – P₁)] + [ρ(v₂² – v₁²)/2] + ρg[z₂ – z₁] = 0

ΔP + [1237 (23.8464² – 1.84²)/2] + (1237×9.8×-3.08) = 0

ΔP + 349,616.522 – 37,337.608 = 0

ΔP + 312,278.914 = 0

ΔP = – 312,278.914 Pa

ΔP = (P₂ – P₁) = -312,278.914

P₂ = 131,722.5 Pa

P₁ = ?

131,722.5 – P₁ = -312,278.914

P₁ = 131,722.5 + 312,278.914 = 444,001.414 Pa

P₁ = (444,001.414) ÷ (101325) = 4.382 atm

Hope this Helps!!!

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