Types of Minor Losses in Pipe MCQ Quiz - Objective Question with Answer for Types of Minor Losses in Pipe - Download Free PDF

Concept:

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

The various losses are given by 

1). Sudden expansion loss:

\({\left( {{h_L}} \right)_{exp}} = \frac{{{{\left( {{v_1} - {v_2}} \right)}^2}}}{{2g}}\)

2). Exit loss:

\({\left( {{h_L}} \right)_{exit}} = \frac{{v^2}}{{2g}}\)

3). Entrance loss:

\({\left( {{h_L}} \right)_{ent}} = \frac{{0.5 \;×\; v^2}}{{2g}}\)

Explanation:

Energy (Head) Losses in Fluid Flow

Definition: Energy losses in fluid flow refer to the reduction in total mechanical energy (head) of the fluid as it moves through a piping system. These losses are due to various factors such as friction, changes in velocity, and obstructions within the pipe. These losses are typically categorized into major and minor losses. Major losses are primarily due to friction in the pipe, while minor losses are caused by fittings, bends, valves, and other components that disrupt the flow.

Correct Option Analysis:

The correct option is:

Option 3: Loss due to friction

Friction loss is not considered a minor energy loss. It is a major loss that occurs due to the friction between the fluid and the pipe wall over the length of the pipe. The Darcy-Weisbach equation is commonly used to calculate this loss:

h_f = f * (L/D) * (V^2 / 2g)

where:

• h_f = frictional head loss
• f = Darcy friction factor
• L = length of the pipe
• D = diameter of the pipe
• V = velocity of the fluid
• g = acceleration due to gravity

Friction losses are significant and often the largest component of total head loss in long pipes. They are influenced by factors such as the pipe material, fluid viscosity, flow velocity, and pipe diameter. Proper management of friction losses is crucial for the efficient design of fluid systems, ensuring that energy consumption is minimized and the desired flow rates are achieved.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Loss due to enlargement

This is a minor energy loss. It occurs when there is a sudden enlargement in the pipe diameter, causing a rapid decrease in fluid velocity and an associated increase in pressure. The energy loss due to enlargement can be estimated using the equation:

h_e = (V_1 - V_2)^2 / 2g

where:

• h_e = head loss due to enlargement
• V_1 = velocity in the smaller section of the pipe
• V_2 = velocity in the larger section of the pipe
• g = acceleration due to gravity

Option 2: Loss due to obstruction in pipe

This is also a minor energy loss. Obstructions such as valves, bends, and fittings in the pipe can cause localized disturbances in the flow, leading to additional energy losses. The head loss due to obstructions can be calculated using the equation:

h_o = K * (V^2 / 2g)

where:

• h_o = head loss due to obstruction
• K = loss coefficient specific to the type of obstruction
• V = velocity of the fluid
• g = acceleration due to gravity

Option 4: Loss due to contraction

This is another example of a minor energy loss. It occurs when there is a sudden contraction in the pipe diameter, causing an increase in fluid velocity and a corresponding decrease in pressure. The energy loss due to contraction can be estimated using the equation:

h_c = (V_2 - V_1)^2 / 2g

where:

• h_c = head loss due to contraction
• V_1 = velocity in the larger section of the pipe
• V_2 = velocity in the smaller section of the pipe
• g = acceleration due to gravity

Conclusion:

Understanding the differences between major and minor energy losses in fluid flow is essential for designing efficient piping systems. Major losses, primarily due to friction, play a significant role in long pipes, while minor losses are associated with localized disturbances such as enlargements, contractions, and obstructions. Proper management of both types of losses is crucial for optimizing energy consumption and ensuring the desired fluid flow rates are achieved within the system.

Explanation:

Minor Losses: 

These occur due to various fittings, valves, bends, elbows, tees, inlets, exits, contractions, and expansions.

Usually expresses in terms of the loss coefficient KL or resistance coefficient, \({h_L} = {K_L}\frac{{{V^2}}}{{2g}}\)

Head loss due to friction in pipe is a major loss.

Additional Information 

Major Losses

Due to friction

• ​When fluid flows from one section to another, there is a reduction in total energy due to friction between the pipe wall and the flowing fluid.
• It is given by Darcy Weisbach Equation: 

​\({h_f} = \frac{{4f'L{V^2}}}{{2gD}} = \frac{{fL{V^2}}}{{2gD}}\)

where, L = length of pipeline,  f’ = friction coefficient,  D = diameter of pipe, V = average velocity, f = friction factor

f’ is a dimensionless quantity whose value depends upon the roughness coefficient of pipe surface and Reynold's number of the flow.​​

Explanation:

Minor Losses

• The losses occur due to various fittings, valves, bends, elbows, tees, inlets, exits, and contractions.

1. Loss of head at the exit of pipe: \(h_L=\frac{V^2}{2g}\) 
2. Loss of head due to obstruction in the pipe: \(h_L=[\frac{A}{C_C(A-a)}-1]^2\times\frac{V^2}{2g}\)
3. Loss of head at the entrance of the pipe with a sharp-cornered entrance: \(h_L=k\frac{V^2}{2g}\)

 Additional InformationMajor Losses due to friction

• When fluid flows from one section to another, there is a reduction in total energy due to friction between the pipe wall and the flowing fluid. 
• It is given by Darcy Weisbach equation: \(h_L=\frac{4f'LV^2}{2gD}\) where, L = length of the pipeline, f' = friction coefficient, D = diameter of the pipe, V = average velocity.

Concept:

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

The various losses are given by 

1). Sudden expansion loss:

\({\left( {{h_L}} \right)_{exp}} = \frac{{{{\left( {{v_1} - {v_2}} \right)}^2}}}{{2g}}\)

2). Exit loss:

\({\left( {{h_L}} \right)_{exit}} = \frac{{v^2}}{{2g}}\)

3). Entrance loss:

\({\left( {{h_L}} \right)_{ent}} = \frac{{0.5 \;×\; v^2}}{{2g}}\)

Hence, the correct relation between the Loss of head at the entrance of a pipe (hi) and Loss of head at the exit of pipe (ho):

hi = 0.5 ho

Explanation:

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;\({V_{avg}} = \frac{1}{{8\mu }}\left( { - \frac{{\delta P}}{{\delta x}}} \right){R^2} = \frac{1}{{32\mu }}\left( { - \frac{{\delta P}}{{\delta x}}} \right){D^2}\)

\(\Longrightarrow \frac{1}{{32\mu }}\left( {\frac{{{p_1} - {p_2}}}{L}} \right){D^2} = {V_{avg}}\)

\(\Longrightarrow \frac{{{p_1} - {p_2}}}{{\rho g}} = \frac{{32\mu {V_{avg}}}}{{\rho g{D^2}}}\)

\(\Longrightarrow \frac{{{p_1} - {p_2}}}{{\rho g}} = \frac{{128\mu {Q}}}{{\pi ×\rho g{D^4}}}\)

Now, ΔP = γ × Hl

Putting ΔP, from the above equation, we get

Hl ∝ \(1 \over D^4\)

From the above expression, it is clear that hydraulic gradient is inversely proportional to D4

Confusion PointsThe above equation is called Hagen–Poiseuille equation, which is valid for only laminar flow in a circular pipe, (as asked in the question), and pressure or head loss is due to the viscous effect of the liquid.

While the Darcy formula, is valid for both laminar and turbulent flow in circular or noncircular sections, pressure loss is due to friction only.

So, when the Darcy formula is available, pressure difference Δ P  1/D5

Concept:

Equation of continuity: A₁V₁ = A₂V₂

A = area of cross section = \(\frac{\pi }{4}{D^2}\)

Head loss due to sudden expansion = \(\frac{{{{\left( {{V_1} - \;{V_2}} \right)}^2}}}{{2g}}\)

Where, V₁ = velocity before expansion

V₂ = velocity after expansion

g = acceleration due to gravity

Calculation:

Given, D₁ = 8 cm, D₂ = 16 cm

Using continuity equation:

\(d_1^2{V_1} = d_2^2{V_2}\)

\({V_2} = {\left( {\frac{8}{{16}}} \right)^2}{V_1}\)

\({V_2} = \frac{1}{4}{V_1}\)

Therefore, head loss,

\({H_l} = \frac{{{{\left( {{V_1} - {V_2}} \right)}^2}}}{{2g}} = \frac{{V_1^2{{\left( {1 - \frac{1}{4}} \right)}^2}}}{{2g}} = \frac{{V_1^2\left( {\frac{9}{{16}}} \right)}}{{2g}}\)

\(H_l=\frac{9}{{16}}\left( {\frac{{V_1^2}}{{2g}}} \right)\)

Concept:

Loss of head due expansion,

\({h_L} = \frac{{{{\left( {{V_1} - {V_2}} \right)}^2}}}{{2g}}\)

Calculation:

Given:

D₁ = 6 cm, D₂ = 12 cm

We know,

A₁V₁ = A₂V₂

\(\Rightarrow \frac{\pi }{4}D_1^2{V_1} = \frac{\pi }{4}D_2^2{V_2}\)

\(\Rightarrow {V_2} = {\left( {\frac{{{D_1}}}{{{D_2}}}} \right)^2}{V_1}\)

\(\Rightarrow {V_2} = \frac{1}{4}{V_1}\)

Loss of head due expansion,

\(\therefore {h_L} = {\left( {\frac{({{V_1} - {V_2}})^2}{{2g}}} \right)} = {\left( {\frac{({{V_1} - \frac{1}{4}{V_1}})^2}{{2g}}} \right)}\)

\(\Rightarrow {h_L} = \frac{9}{{16}}\frac{{V_1^2}}{{2g}}\)

Concept:

Types of losses in pipe:

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 a significant loss of energy because of friction.

According to Darcy’s Weisbach equation, A major loss (h_L) is the head loss due to friction

\({h_L} = \frac{{fL{V^2}}}{{2gD}}\)

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

Calculation:

Given data

D = 12 cm

f = 0.04

Minor losses =  \(5 \frac{V^2}{2g}\)

Loss due to friction(h_L)

\({h_L} = \frac{{fL{V^2}}}{{2gD}}\)

To account for the minor losses

\( \frac{{fL{V^2}}}{{2gD}} = 5 \frac{V^2}{2g}\)

\({fL \over D} = 5\)

\(L = {5 \times D \over f} = {5 \times 0.12 \over 0.04}\) = 15 m

Concept

Power required to run a pump \(=\rho\times Q\times g\times(H+h_f)\)

\(\rho\) = Density, Q = Discharge through pump, H = head, liquid to be pumped, h_f= friction head

Calculation:

Given: g =10 m²/s; Q = 0.2 m³/s; H = 10 m, h_f=5 m

Power required to run a pump 

\(=\rho\times Q\times g\times(H+h_f)\)

\(=1000\times 0.2\times 10\times(10+5)\)

\(=30000W\)

\(=30kW\)

Explanation:

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,

\(K_L~=~\frac{h_L}{\frac{V^2}{2g}}\)

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

Additional Information

Major losses: Whenever the losses in the pipes are because of friction they are considered as major losses because there is a significant loss of energy because of friction.

According to Darcy’s Weisbach equation:

Major loss (hL): this is the head loss due to friction.

\({h_L} = \frac{{fL{V^2}}}{{2gD}}\)

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

Explanation:

Pipes in parallel:

If the main pipe divides into two or more branches and again join together downstream to form a single pipe, then the branched pipes are said to be connected in parallel (compound pipes).

• The rate of flow in the main pipe is equal to the sum of the rate of flow through branch pipes
• The loss of head for each branch pipe is the same

\({\rm{head\ loss\ h}} = {{\rm{h}}_{{{\rm{L}}_1}}} = {{\rm{h}}_{{{\rm{L}}_2}}} = {{\rm{h}}_{{{\rm{L}}_3}}}\)

\({h_f}_L = \frac{{{f_1}{L_1}V_1^2}}{{2g{D_1}}} = \frac{{{f_2}{L_2}V_2^2}}{{2g{D_2}}} = \frac{{{f_3}{L_3}V_3^2}}{{2g{D_3}}}\)

Important Points

Pipes in series:

Pipes in series or compound pipes are defined as the pipes of different lengths and different diameters connected end to end (in series) to form a pipeline.

• Discharge through each pipe is the same
• The total loss of energy or head loss will be the sum of the losses in each pipe

Explanation: 

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. 

Flow separation actually occurs during sudden expansions, not contractions. In sudden contractions, the flow accelerates, and while there might be some turbulence and potential minor separations if the contraction is very abrupt, the major issue in sudden expansions is the flow separation due to a backflow and vortex formation as the fluid tries to fill the larger pipe diameter.

Explanation: 

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.

Calculation:

D2 = 2‘D1

Calculation:

Given, D1 = D cm, D2 = 2D cm

Using continuity equation:

\(D_1^2{V_1} = D_2^2{V_2}\)

\({V_2} = \frac{1}{4}{V_1}\)

Therefore, head loss,

\({H_l} = \frac{{{{\left( {{V_1} - {V_2}} \right)}^2}}}{{2g}} = \frac{{V_1^2{{\left( {1 - \frac{1}{4}} \right)}^2}}}{{2g}} = \frac{{V_1^2\left( {\frac{9}{{16}}} \right)}}{{2g}}\)

\(H_l=\frac{9}{{16}}\left( {\frac{{V_1^2}}{{2g}}} \right)\)

\(H_l=\frac{9}{{16}}\left( {\frac{{16V_2^2}}{{2g}}} \right)\)

\(H_l = \rm \frac{9V_2^2}{2g}\)

Explanation:

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;

\({V_{avg}} = \frac{1}{{8\mu }}\left( { - \frac{{\delta P}}{{\delta x}}} \right){R^2} = \frac{1}{{32\mu }}\left( { - \frac{{\delta P}}{{\delta x}}} \right){D^2}\)

\(\Longrightarrow \frac{1}{{32\mu }}\left( {\frac{{{p_1} - {p_2}}}{L}} \right){D^2} = {V_{avg}}\)

\(\Longrightarrow \frac{{{p_1} - {p_2}}}{{ρ g}} = \frac{{32\mu {V_{avg}}}}{{ρ g{D^2}}}\)

\(\Longrightarrow \frac{{{p_1} - {p_2}}}{{ρ g}} = \frac{{128\mu {Q}}}{{\pi ×ρ g{D^4}}}\)

Now, ΔP = ρ g Hl

Putting ΔP, from the above equation, we get

Hl ∝ \(1 \over D^4\)

From the above expression, it is clear that hydraulic gradient is inversely proportional to D4