Friction Loss (Darcy Weisbach Equation) MCQ Quiz in मराठी - Objective Question with Answer for Friction Loss (Darcy Weisbach Equation) - मोफत PDF डाउनलोड करा

Explanation:

​Head losses in pipes:

• The reduction in the total head (sum of elevation head, velocity head, and pressure head) of the fluid as it moves through a fluid system is referred to as head loss.
• In real fluids, the head loss is unavoidable. It is present because of:
  • the friction between the fluid and the walls of the pipe.
  • the friction between adjacent fluid particles as they move relative to one another.
  • the turbulence caused by such components as piping entrances and exits, pumps, valves, flow reducers, and fittings.
• Although the head loss represents an energy loss, it does not represent a loss of the fluid's total energy. As a result of the law of conservation of energy, the total energy of the fluid conserves. In reality, the frictional head loss causes a corresponding increase in the fluid's internal energy (temperature).
• Head loss of the piping system is divided into two main categories:
  • Major Head Loss – due to friction in pipes and ducts.
  • Minor Head Loss – due to components as valves, fittings, bends and tees.
• In most engineering flows, the major head loss is roughly proportional to the square of the flow rate and is given by Darcy–Weisbach equation.
  \(\mathbf{\frac{\Delta h }{L}~=~\frac{fV^2}{2gD}}\)

where Δh is the head loss in m, f is Darcy friction factor, L is the pipe length, D is the hydraulic diameter and V is the mean flow velocity.

• An increase in velocity causes the flow to transition to turbulent flow and this turbulence causes the formation of eddies of many different length scales. These formations come at the expense of the available energy loss of the flow.
• The large-scale eddies contain the majority of the kinetic energy of turbulent motion. Some portion of this energy is dissipated when these large scale eddies are converted into small scale due to the viscous effects.

Explanation:

The Darcy-Weisbach equation is one of the most commonly used equations for estimating frictional pressure drops in internal flows.

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

Where f is the friction factor which depends on the Reynolds number (Re = ρVD/μ).

Explanation:

Turbulent flow – Turbulent flow occurs at relatively larger velocities and is characterized by chaotic behaviour, irregular motion, large mixing and eddies. For such flows, inertial effects are more pronounced than the viscous effects.

• Mathematically the velocity field of turbulent flow is represented as\(V = \bar V + V'\) or the velocity fluctuates at small time scales around a large time-averaged velocity.
• Similarly,  \(P = \bar P + P',T = \bar T + T'\)etc.
• Parameter Reynolds number \(\left( {\frac{{\rho vd}}{\mu }} \right)\) is used to characterize Laminar and Turbulent flow.
• If Re < 2100 for pipe flow the flow is laminar and if Re > 104 the flow is turbulent.

For Turbulent flow, the velocity or pressure field may not be exactly (Analytically) represented. So we will solve it using dimensional analysis.

   \({\rm{\Delta }}P = {\rm{\Delta }}P\left( {D,L,\overline {V,} \rho ,\mu ,\varepsilon } \right)\)      where ε = Surface roughness

\(\frac{{{\bf{\Delta }}P}}{{\rho \overline {{V^2}} }} = f\left( {\frac{{\rho vd}}{\mu },\frac{L}{D},\frac{\varepsilon }{D}} \right) = f\left( {{R_e},\frac{L}{D},\frac{\varepsilon }{D}} \right)\),  the turbulent flow through the pipe turbulent pressure drop or head loss is a function of the square of velocity.

• The experimental observations suggest that pressure drop in the pipe flow under turbulent conditions depends upon Reynolds number and surface roughness.

Concept:

The water is flowing through the pipe. The head loss is given as,

\({\bf{h}} = \frac{{4{\bf{fl}}{{\bf{v}}^2}}}{{2{\bf{gD}}}}\)

Calculation:

Given: D = 500 mm = 0.5 m, l = 981 m, v = 2 m/s, f = 0.008

\({\bf{h}} = \frac{{4 × 0.008 × 981 × {2^2}}}{{2 × 9.81 × 0.5}} = 12.8~{\bf{m}}\)

Use 4f instead of "f" because the magnitude given f = 0.008 is less. So, It is fanning factor and friction factor = 4×fanning factor 

Concept:

A momentum correction factor is defined as the ratio of momentum of the flow per second based on actual velocity to the momentum of the flow per second based on average velocity across a section.

\({\rm{\beta }} = \frac{{{\rm{Momentum\;per\;second\;based\;on\;actual\;velocity}}}}{{{\rm{Momentum\;per\;second\;based\;on\;average\;velocity}}}}\)

It is considered to take into the effect of the non-uniform distribution of flow through pipes.

Important Points

Concept:

Darcy friction factor is define as,

\({\rm{f}} = \frac{{64}}{{{\rm{Re}}}}{\rm{\;where}},{\rm{\;Re}} = {\rm{Raynolds\;no}}.{\rm{\;}}\)

\({\rm{\;Re}} = \frac{{{\rm{\rho VD}}}}{{\rm{\mu }}} = \frac{{{\rm{VD}}}}{{\rm{\nu }}}\)

where, ρ = density of fluid, V = velocity of fluid, D = Diameter of pipe,

v = kinematic viscosity

If Re > 4000 then the flow become turbulent flow

If Re < 2000 then the flow become laminar flow

Calculation:

Given: D = 10 cm = 0.1 m, v = 0.1 m/s, v = 10-5 m2/s 

\({\rm{Re}} = \frac{{0.1 × 0.1}}{{{{10}^{ - 5}}}} = 1000{\rm{\;}}\)

Therefore, it is laminar flow

\({\rm{f}} = \frac{{64}}{{1000}} = 0.064\)

For plate,

If Re > \(5 \times {10^5}\) then the flow become turbulent flow

If Re < \(5 \times {10^5}\) then the flow become laminar flow

Explanation:

Losses in pipe: 2 type

Major loss: Major loss occurs only due to friction.

Minor loss: Depend on different factors.

Major loss: 

Major loss in the pipe due to friction is given by the Darcy-Weisbach equation.

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

Here, L = length of pipe

D = dia of pipe

V = mean velocity

f = friction factor (0.02 to 0.04 for metals)

hf = head loss due to friction

Minor loss:

Different type of minor losses in pipe

Explanation:

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 a significant loss of energy because of friction.

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) = 60 m

The velocity of flow (v) = 2.5 m/s

Friction factor (f) = 0.005 × 4 

Head loss due to friction (hf) =?

\(h_{f}={0.005\times 4× 60× 2.5^2\over 2× 9.81× 0.2}\) = 1.91 m

Explanation:

The darcy-Weisbach formula for head loss due to friction is,

\(h_f = \dfrac{4flV^2}{2gd}\)

where, f = Darcy's coefficient of friction, l = length of the pipe, v = velocity of the fluid in the pipe, d = diameter of the pipe.