Test: Types of Minor Losses in Pipe - Civil Engineering (CE) MCQ

Concept:
Pumping power required to pump water to a height of H against head loss h_f is given by :
Power  P = γ_w Q(H + h_f)
Whereγw = unit weight of  water, Q = Rate of flow, H = Pumping height, h_f = friction and other minor losses
Due to losses, total height against which power is required = H + h_f
Solution:
Given, Pumping height (H) = 10 m, Total Head Loss (h_f) = 5 m, Rate of flow (Q) = 0.1 m³/sec and γ_w = = 9.81 kN/m³
Pumping Power required to lift water:
P = γ_w Q(H+h_f) = 9.81 × 10³ × 0.1 × (10 + 5) = 14.715 × 10³ W
P = 14.715 kW
Therefore pumping power required is 14.715 kW

Laminar flow through a circular pipe:
In a constant diameter pipe, the pressure drops uniformly along the pipe length (except for the entrance region)
∵ we know that the average velocity through a circular pipe;

Now, ΔP = ρ g H_l
Putting ΔP, from the above equation, we get
H_l ∝ 1 / D⁴
From the above expression, it is clear that hydraulic gradient is inversely proportional to D⁴

Minor head losses:

• Head loss at entry
  
• Head loss due to expansion
  
• Head loss at exit
  

Minor loses caused by the disruption of the flow due to the installation of appurtenances, such as valves, bends, and other fittings.

• Minor losses are usually expressed in terms of the loss coefficient K_L also called the resistant coefficient and it is defined as,

where K_L = loss coefficient, H_L = loss of head, V = velocity of fluid

• In some cases, the minor losses may be greater than the major losses, for example, in a system where several turns and valves in a short distance.

Following are some minor losses which occur in pipe flow:

• Loss of energy due to sudden enlargement
• Loss of energy due to sudden contraction
• Loss of energy at the entrance of the pipe
• Loss of energy at the exit from pipe
• Loss of energy in Bends and Pipe Fittings

There are generally two types of losses

• Minor losses
• Major losses

Minor losses: Whenever there is a change in the cross-section, minor losses occur.
For e.g. sudden expansion, sudden contraction or bend in the pipes.
Major losses: Whenever the losses in the pipes are because of friction they are considered as major losses because there is significant loss of energy because of friction.
According to Darcy’s Weisbach equation:
Major loss (hL): this is the head loss due to friction.

where f = friction factor, L = length of pipe, V = velocity of flow, D = diameter of the pipe

There are generally two types of losses that occur in a pipe flow problem:

1. Major loss: Major head loss occurs due to friction, which is given by:
   • h_f = flv² / 2gd
   • Where f = friction factor = 64Re
2. Minor head loss: Minor head loss occurs due to:
   1. Sudden enlargement
   2. Sudden contraction
   3. Due to pipe bends
   4. head loss at the entrance and exit of pipe etc.

Loss Due To Sudden Expansion: It is a type of minor loss at the end of a pipe or when smaller diameter pips meet large diameter pipe due to sudden enlargement in the area of flow. It is larger than loss due to sudden contraction because Eddies are formed at the entrance of a large diameter pipe.


Loss Due To Sudden Contraction: It is a type of minor loss when a large diameter pipe meets a small diameter pipe or a small diameter pipe attached to a water reservoir due to a sudden decrease in the area of flow. Separation of flow occurs at the entrance of a small diameter pipe.

The major loss for the flflow through the pipes is due to the frictional resistance between adjacent fluid layers sliding over each other. All other losses are considered to be minor losses.

According to the laws of fluid friction, r_f / v (for steady streamline flow) and r_f / v₂(for turbulent flow), where rf is the frictional resistance and v is the velocity of flow.

According to the laws of fluid friction, the frictional resistance is proportional to the surface area of contact for both laminar and turbulent flows.