Question

Crude oil of density 925 kg/m³ and absolute viscosity 0.065 N.s/m² at 20°C is pumped through a horizontal pipeline 100 mm in diameter at a rate of 10 liters per second. Answer the following:

The friction factor of the pipe is:
a) 0.354
b) 0.0431
c) 0.0354
d) 0.431

Answer 1

To calculate the friction factor of the pipe, you can use the Darcy-Weisbach equation which relates the friction factor to the Reynolds number.

Step-by-step explanation:

To calculate the friction factor of the pipe, we can use the Darcy-Weisbach equation which relates the friction factor to the Reynolds number.

The Reynolds number can be calculated using the equation: Re = (u * d) / v, where u is the velocity of the fluid, d is the diameter of the pipe, and v is the viscosity of the fluid. In this case, the flow rate is given as 10 liters per second which can be converted to cubic meters per second. The velocity can be calculated as Q / A, where Q is the flow rate and A is the cross-sectional area of the pipe. The cross-sectional area can be calculated as π * (d/2)^2.

Plug in the values into the equation to get the Reynolds number. Once you have the Reynolds number, you can use a Moody chart or Colebrook-White equation to find the friction factor. For laminar flow, the friction factor is given by f = 64 / Re.

Calculating the Reynolds number:

• d = 100 mm = 0.1 m
• Q = 10 L/s = 0.01 m^3/s
• A = π * (0.1/2)^2 = 0.00785 m^2
• u = Q / A = 0.01 / 0.00785 = 1.273 m/s
• Re = (u * d) / v = (1.273 * 0.1) / 0.065 = 1.956

Since the Reynolds number is less than 2000, the flow is laminar. Therefore, the friction factor is given by f = 64 / Re = 64 / 1.956 = 0.0327.