Question:
Water flows under pressure through a horizontal pipe. The pipe diameter is D=0.2 m and the pipe roughness height
is $k_s = 2.X \times 10^{-4}$ m. The flow rate of the flow through the pipe is Q=0.0628 m³/s. The dynamic viscosity of the fluid is
$\mu = 10^{-3}$ N s/m² and its specific mass is $\rho = 1000$ kg/m³. If the pressure drop per unit length in the direction of the flow
is $\frac{dp}{dx} = \frac{3X}{m} \frac{N/m^2}{m} (30 + X \frac{N/m^2}{m})$; Please compute:
a) Cross-sectional average velocity of the flow,
b) Type of the flow (Laminar or Turbulent),
c) Wall shear stress,
d) Shear velocity,
e) Viscous sublayer thickness ($\delta$),
f) Determine the hydraulic behavior of the pipe by calculating the Roughness Reynolds number
$(N_{R*} = \frac{u_* k_s}{\nu})$ defined by the shear stress.
g) Check the hydraulic behavior of the pipe by comparing the viscous sublayer thickness with
the roughness height.
