Fluid Dynamics MCQ Quiz in मल्याळम - Objective Question with Answer for Fluid Dynamics - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

Bernoulli’s Equations

At Section 1 

\(\frac{{{p_1}}}{{\rho g}} + \frac{{V_1^2}}{{2g}} + {z_1}\)

At Section 2

\(\frac{{{p_2}}}{{\rho g}} + \frac{{V_2^2}}{{2g}} + {z_2}\)

Calculation:

Given:

P₁ = 100 kPa, Z₁ = 10 m, P₂ = 75 kPa, z₂ = 12 m, v = 4 m/s, d = 500 mm = 0.5 m

At Section 1 

\(\frac{{{p_1}}}{{\rho g}} + \frac{{V_1^2}}{{2g}} + {z_1} = \frac{{100 \times {{10}^3}}}{{1000 \times 10}} + \frac{{{4^2}}}{{2 \times 10}} + 10 = 20.8\;m\)

At Section 2

\(\frac{{{p_2}}}{{\rho g}} + \frac{{V_2^2}}{{2g}} + {z_2} = \frac{{75 \times {{10}^3}}}{{1000 \times 10}} + \frac{{{4^2}}}{{2 \times 10}} + 12 = 20.3\;m\)

(Total Energy) 1 > (Total Energy) 2

∴ Flow takes place from section 1 to section 2 with a head loss of 0.5 m.

Explanation:

In a fluid, the following forces are present.

Fg due to gravity force

Fp due to pressure force

Fν due to viscosity

Fs due to surface tension

Ft due to turbulence.

Fc due to compressibility.

∴ F_net = F_g + F_p + F_v + F_t + F_s + F_e

Now,

If F_net = F_g + F_p + F_ν + F_t this is known as Reynold’s equations of motion.

If F_net = F_g + F_p + F_ν this is known as Navier-Stokes equation of motion.

If F_net = F_g + F_p this is known as Euler’s equation of motion.

​Explanation:

Euler's equation of motion:

The Euler's equation for a steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure and density of a moving fluid. It is based on the Newton's Second Law of Motion which states that if the external force is zero, linear momentum is conserved. The integration of the equation gives Bernoulli's equation in the form of energy per unit weight of the following fluid.

It is based on the following assumptions:

• The fluid is non-viscous (i,e.,inviscid fluid or the frictional losses are zero)
• The fluid is homogeneous and incompressible (i.e., the mass density of the fluid is constant)
• The flow is continuous, steady and along the streamline.
• The velocity of the flow is uniform over the section.
• No energy or force (except gravity and pressure forces) is involved in the flow.

As there is no external force applied (Non-viscous flow), therefore linear momentum will be conserved.

Concept:

Bernoulli’s Equation is known as the conservation of energy principle and states that in a steady, ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant. The total energy consists of pressure energy, kinetic energy and potential energy or datum energy

From Bernoulli’s equation,

Pressure head + kinetic head + potential head = constant

\(\frac{{{P_1}}}{{\rho g}} + \frac{{v_1^2}}{{2g}} + {z_1} = \frac{{{P_2}}}{{\rho g}} + \frac{{v_2^2}}{{2g}} + {z_2} + {h_L}\)

h_L = head loss

For a horizontal pipe,

Changes in the kinetic and potential head are negligible.

\(\frac{{{P_1}}}{{\rho g}} = \frac{{{P_2}}}{{\rho g}} + {h_L}\)

Calculation:

Given:

P₁ = 3 kgf/cm², P₂ = 2.6 kgf/cm²

1 kgf/cm² = g N/cm² = g × 10⁴ N/m²

P₁ – P₂ = 0.4 kgf/cm² = 0.4g × 10⁴ N/m²

\(\frac{{{P_1}}}{{\rho g}} = \frac{{{P_2}}}{{\rho g}} + {h_L}\)

\({h_L} = \frac{{{P_1} - {P_2}}}{{\rho g}} = \frac{{0.4 \times g \times {{10}^4}}}{{{{10}^3} \times g}} = 4\;m\)

Explanation:

1. Static pressure:  It is the actual thermodynamic pressure of the fluid and does not incorporate any dynamic effects i.e. P.

2. Dynamic pressure: It represents the pressure rise when the fluid in motion is brought to a stop isentropically i.e. \(\frac{ρ V^2}{2}\).

3. Hydrostatic pressure: Pressure at a point in the fluid due to its weight and it depends on the reference selected i.e. ρgh.

4. Total pressure: Sum of all the pressures i.e. P + \(\frac{ρ V^2}{2}\) + ρgh.

5. Stagnation pressure: Sum of static pressure and dynamic pressure i.e. P + \(\frac{ρ V^2}{2}\).

Venturi meter:

• It is a device in which pressure energy is converted into kinetic energy and is used to measure the rate of flow through a pipe.
• The venturi meter basically works on the principle of Bernoulli’s equation.
• It consists of a converging portion, throat, and diverging portion.
• When the fluid reaches the converging part then according to the continuity equation when the cross-sectional area decreases then the velocity of the flowing fluid increases.
• Bernoulli’s equation says that when the velocity of the flowing fluid increases the pressure of the flowing fluid decreases.
• Hence, the venturi meter has the lowest pressure drop for a given range of flow.

Concept:

Pressure due to 'h' m column of fluid (P) = ρgh

Calculation:

Given:

ρ = 1000 kg/m³, g = 10 m/s², P = 1.4 MPa = 1.4 ×10⁶ N/m²

P = ρgh

1.4 × 10⁶ = 1000 × 10 × h

∴ h = 140 m

Hence depth is approximately 140 m.

Explanation:

In a fluid, the following forces are present

Gravity force (F_g) due to gravity

Pressure force F_p due to pressure of fluid

Viscous force F_ν due to viscosity

Tension force F_s due to surface tension

Turbulent force F_t due to turbulence.

F_c due to compressibility.

∴ F_net = F_g + F_p + F_ν + F_s + F_t + F_c

• If F_net = F_g + F_p + F_ν + F_t this is known as Reynold’s equations of motion.
• If F_net = F_g + F_p + F_ν this is known as Navier-Stokes equation of motion.
• If F_net = F_g + F_p this is known as Euler’s equation of motion.

Explanation:

Bernoulli equation has been obtained on the assumptions that the fluid is ideal and the flow is steady. Therefore, the Bernoulli equation is nothing but the law of conservation of energy. This equation includes the pressure (or flow) and kinetic and potential energy. Accordingly the terms pressure head, velocity head and potential head (also called the datum head) are used. Sum of the pressure and potential head is called the piezometric head and sum of all the heads is named as the total head. Thus according to the Bernoulli equation, the total head is constant throughout the flow.

Bernoulli's equation along streamlines:

\(\frac{P}{{\rho g}} + \frac{{{v^2}}}{{2g}} + Z = constant\)

Elevation head: Z

Pressure head: P/ρg

Velocity head: v²/2g

Piezometric head: (P/ρg) + Z = Hydraulic grade line (HGL)

Total head: (P/ρg) + (v²/2g) + Z = Energy grade line (EGL)

\(\frac{P}{{\rho g}} + Z + \frac{{{v^2}}}{{2g}} = constant\)

Piezometric head + Velocity head = constant

So, as per the above explanation, the total head i.e. Pressure head, Velocity head, Piezometric head are constant. It means, for total head to be constant, each head should be constant. Therefore, in fluid flow, the line of constant piezometric head passes through two points that have the constant Velocity head. 

Thus, the line of constant piezometric head passes through two points which have the same velocity.

Concept:

For orifice in tank,

\(V=\sqrt {2gh} \)

∴ \(Q = a \times V={C_d}a\sqrt {2gh} \)

Where,

Q = Discharge

V = Velocity

C_d = Coefficient of discharge

h = Depth of orifice

a = Area of cross section of orifice

Solution:

D₁ = 1 cm

D₂ = 2 cm

Discharge, \(Q = {C_d}a\sqrt {2gh} \)

\(\frac{{{Q_1}}}{{{Q_2}}} = \frac{{{a_1}\sqrt {{h_1}} }}{{{a_2}\sqrt {{h_2}} }} = \frac{1}{4}\sqrt {\frac{{{h_1}}}{{{h_2}}}} \)