Question

Water at 20 °C (p=998 kg/m^3 and = 1.002x10^-3 kg/ ms) is flowing steadily in a 35 m long and 4 cm diameter horizontal pipe made of stainless steel at a rate of 10 Ls. The flow in the pipe is redirect at 90° using an elbow which has the same diameter as the pipe. Determine: (a) the Reynolds Number (b) the major head loss, (c) the minor head loss, and (d) the power required to overcome this pressure drop

Answer 1

To determine the Reynolds Number, we need to calculate the velocity of the water in the pipe and the diameter of the pipe. The major head loss can be calculated using the Darcy-Weisbach equation. The minor head loss can be calculated using the equation for head loss through an elbow.

Step-by-step explanation:

To determine the Reynolds Number, we need to calculate the velocity of the water in the pipe and the diameter of the pipe. The velocity of the water can be found by converting the flow rate of 10 L/s to m³/s (1 L = 0.001 m³). The diameter of the pipe is given as 4 cm, which can be converted to meters. The Reynolds Number can then be calculated using the formula: Reynolds Number = (density x velocity x diameter) / viscosity.

To calculate the major head loss, we can use the Darcy-Weisbach equation: head loss = (friction factor x length x velocity²) / (2 x gravity x diameter).

To calculate the minor head loss, we can use the equation for head loss through an elbow: head loss = (K x velocity²) / (2 x gravity), where K is the loss coefficient for the elbow.

The power required to overcome the pressure drop can be calculated using the equation: power = (pressure drop x flow rate) / (density x efficiency).