Flow Through Pipes MCQ Quiz in मराठी - Objective Question with Answer for Flow Through Pipes - मोफत PDF डाउनलोड करा

Explanation:

Head loss due to sudden enlargement

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

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

from the continuity equation,

\(\frac{{{V_2}}}{{{V_1}}} = \frac{{{A_1}}}{{{A_2}}}\)

\(\begin{array}{l} {h_L} = {\left( {1 - \frac{{{A_1}}}{{{A_2}}}} \right)^2}\frac{{V_1^2}}{{2g}}\;\\ {h_L} = {k_e}\;\frac{{V_1^2}}{{2g}} \end{array}\)

Explanation:

The Chezy equation can be used to calculate mean flow velocity in open channel.

Chezy’s constant is given by:

\(C = \sqrt {\frac{{8g}}{f}}\)

f = friction factor

Its unit is \(\frac{\sqrt{m}}{s}\)

So, the dimensions of  Chezy coefficient C is L1/2 T-1

Concept:

The pressure drop head in a laminar flow through the circular pipe is given by:

\(\frac{{{P_1} - {P_2}}}{{ρ g}} = \frac{{32\;μ VL}}{{ρ g{d^2}}}\)

\(Δ P = \frac{{32\;μ VL}}{{{d^2}}}\)

\(\frac{Δ P}{L} = \frac{{32\;μ V}}{{{d^2}}}\)

Where, ΔP = Pressure drop, μ = viscosity of the fluid, V = Mean velocity of flow, L = Length of pipe, D = diameter of the pipe, ρ = Density of the fluid

Concept:

time travelled by pressure wave value from tank to tank from the value

\(t=\dfrac{2L}{C}\)

L → Length of Pipe

C → Velocity of pressure wave

Calculation:

Given:

Velocity of pressure wave (C) = 2 m/s

time travelled by pressure wave value from tank to tank from value

\(t=\dfrac{2L}{C}\)

L → Length of Pipe

C → Velocity of pressure wave

if \(t \ge \dfrac{2L}{C}\) → Gradual closure

\(t \le \dfrac{2L}{C}\) → Sudden closure

So, critical time \(t=\dfrac{2L}{C}=\dfrac{2L}{2}\)     {for unit length}

t = 1 s

Explanation:

Head loss at the entrance of a pipe = \({H_{L\left( {entance} \right)}} = \frac{{0.5{V^2}}}{{2g}}\)

Head loss at the exit of a pipe = \({H_{L\left( {exit} \right)}} = \frac{{{V^2}}}{{2g}}\)

The ratio of head loss at the exit of the pipe to the head loss at the entrance of the pipe is

\(\frac{{{H_{L\left( {exit} \right)}}}}{{{H_{L\left( {entance} \right)}}}} = \frac{{\frac{{{V^2}}}{{2g}}}}{{\frac{{0.5{V^2}}}{{2g}}}} = 2\)

Concept:

Wall shear stress is given by:

\({\rm{}}{{\rm{\tau }}_{\rm{w}}} = - \frac{{\partial {\rm{P}}}}{{\partial {\rm{x}}}}\times\frac{{\rm{R}}}{2}{\rm{}}\)

where \(\frac{{\partial {\rm{P}}}}{{\partial {\rm{x}}}} = pressure~gradient\), R = radius of pipe = D/2

for length L, the pressure drop is ΔP

∴ Pressure gradient is \( \frac{{\partial {\rm{P}}}}{{\partial {\rm{x}}}} = \frac{{{\rm{Δ P}}}}{{{\rm{L}}}}~\)

Wall shear stress is 

\({\rm{}}{{\rm{\tau }}_{\rm{w}}} = - \frac{{\partial {\rm{P}}}}{{\partial {\rm{x}}}}\times\frac{{\rm{R}}}{2}{\rm{}}= \frac{{{\rm{Δ P}}}}{{\rm{L}}}\times \frac{{\rm{D}}}{{2 \times 2}} = \frac{{{\rm{Δ PD}}}}{{4{\rm{L}}}}\)

Explanation:

Darcy-Weisbach Equation

\(h_{f}={fLv^2\over 2gD}\)

Where L = length of pipe 

D = Diameter of pipe

v = Mean velocity of flow

f = Friction factor

\(h_{f}\) = Head loss due to friction

Calculation:

Given data:

Pipe diameter (D) = 200 mm

Length (L) = 50 m

The velocity of flow (v) = 1.5 m/s

Friction factor (f) = 0.018

Head loss due to friction (h_f) =?

\(h_{f}={0.018\times 50\times 1.5^2\over 2\times 9.81\times 0.2}\)

\(h_{f}={2.025\over 3.924}\)

\(h_{f}=0.516\, m\)

Head loss due to friction (\(h_{f}\)) in the given pipe is 0.516 m.

Explanation:

Given data:

Length of the first pipe (L₁) = 1500 m

Diameter of first pipe (D₁) = 50 cm or 0.50 m

Length of the second pipe (L2) = 600 m

Diameter of second pipe (D2) = 40 cm or 0.40 m

Length of the third pipe (L3) = 400 m

Diameter of third pipe (D3) = 30 cm or 0.30 m

Diameter equivalent pipe (D) = 40 cm or 0.4 m

Length of equivalent pipe (L) =?

In series combination length of the equivalent pipe is given by -

\({L\over D^5}={L_{1}\over D_{1}^5}+{L_{2}\over D_{2}^5}+{L_{3}\over D_{3}^5}+...\)

\({L\over 0.4^5}={1500\over 0.5^5}+{600\over 0.4^5}+{400\over 0.3^5}\)

\(L=0.4^5[{1500\over 0.5^5}+{600\over 0.4^5}+{400\over 0.3^5}]\)

\(L=2777.116\, m\)

Hence, the equivalent length of the pipe is 2778 m.

Concept:

Flow-through Pipes: In flow-through pipe different type of losses takes place.

Major losses are due to viscous (friction) resistance through the wall, and head loss due to friction is given by Darcy's Weichback equation: 

​ \(h_f =\frac{fLV^2}{2gD} = \frac{fLQ^2}{12.1\ D^5}\) 

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

Minor losses these losses are due to change in momentum of the fluid due to the sudden expansion or contraction, change in the shape of the pipe.

Compound Pipes: Types of pipe connection are:

In Series Connection of pipe discharge is same and losses are different in each pipe.

• Q₁ = Q₂ = Q₃ = ................ = Q
• Equivalent head h_f = h_f1 + h_f2 + hf2 ....

In Parallel Connection of pipe discharge is different and losses are same in each pipe.

• Q = Q₁ + Q2 + Q₃ ..... + Q
• Equivalent head hf = hf1 = hf2 = hf2 ......

Calculation:

Given:

D₁ = 10 cm, D₂ = 40 cm , same length L₁ = L₂ = L, same friction factor f₁ = f₂ = f

In parallel Connection Head loss in pipe are equal:

h_f1 = hf2

\(\frac{fLQ_1^2}{12.1\ D_1^5} = \frac{fLQ_2^2}{12.1\ D_2^5}\) ⇒ \(\frac{Q_1^2}{(10)^5} = \frac{Q_2^2}{(40)^5}\)

\(\frac{Q_2^2}{Q_1^2} = \frac{(40)^5}{(10)^5}\)

\(\frac{Q_2}{Q_1} = 32\)

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 KL also called the resistant coefficient and it is defined as,

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

where KL = loss coefficient, HL = 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 that occur in pipe flow:
  • Loss of energy due to sudden enlargement
  • Loss of energy due to a 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:Headloss=hf=fLV22gD" id="MathJax-Element-36-Frame" role="presentation" style="display: inline; position: relative;" tabindex="0">

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