Question

Determine the greatest pressure drop allowed over the 10-m-long pipe caused by viscous friction, so the flow remains laminar.

Answer 1

This question is incomplete, the complete question is;

Determine the greatest pressure drop allowed over the 10-m-long pipe caused by viscous friction, so the flow remains laminar.

The 125-mm-diameter smooth pipe is transporting SAE 10W-30 oil with ρ=920 kg/m3 and µ=0.2 N.s/m2 .

Answer: the greatest pressure drop allowed is 14247 Pascals

Explanation:

LAMINAR FLOW INF PIPE

greatest pressure drop

(P1 - P2) = pressure drop

(P1 - P2) = 32uvl / D²

so (P1 - P2) ∝ V

greatest pressure drop is only at very high velocity

now Re (Reynold Number = svd / u

Re ∝ V

so velocity is high when Re is high

Re = 2000 ( Highest for LAMINAR)

Re = 2000 = svd / u

now in the question we were given that

s = 920 kg/m³, u = 0.2 NS/m², d = 125mm = 0.125m, l = 10m

so we substitute;

2000 = (920 × v × 0.125) / 0.2

v = 3.48 m/s

now pressure drop = (P1 - P2) = 32UVL / d²

we substitute

(P1 - P2)  = (32(0.2) (3.48)(10)) / (0.125)²

(P1 - P2) = 14247 Pascals

therefore the greatest pressure drop allowed is 14247 Pascals