Chapter 6, Problem 6.1P

To determine

To show:

Flow is laminar or not.

Answer to Problem 6.1P

Flow is not laminar.

Explanation of Solution

Given Information:

The diameter of pipe is, d=5 cm=0.005m

The flow rate through pipe is, Q = 10⁶ N/h = 277.78 N/s.

Concept Used:

At $20℃$, density of SAE 30W oil is $\rho =891kg/m^3$,

Viscosity of SAE 30W oil is $\mu =0.29kg/(m.s)$

Calculation:

The units of flow rate are converted from N/h to m³ /s.

$Q=277.78N/s.$

$=\frac{277.78}{\rho \times 9.81}$

$=0.032m^3/s$

As per, the definition of Reynolds number:

$\mathrm{Re}=\frac{\rho Vd}{\mu }$

$=\frac{4\rho Q}{\pi d\mu }$, therefore V=Q/A = $\frac{4Q}{\pi d^2}$

$=\frac{4\times 891\times 0.032}{\pi d\mu }$

$=\frac{114.048}{\pi \times 0.05\times 0.29}$

$\mathrm{Re}=2503$

Therefore, flow is not laminar because for laminar flow, $\mathrm{Re}\le 2300$

Conclusion:

Flow is not laminar.