Fluid Mechanics Chapter 4 - Control Volume Analysis

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Questions and Answers

What does the law of conservation of momentum state?

Momentum has no relation to external forces.

Momentum is only conserved in static conditions.

Momentum increase is only permitted in fluid dynamics.

Momentum cannot change unless external forces are applied. (correct)

What is the formula for momentum represented as?

Momentum $M = mgh$

Momentum $M = rac{dM}{dt}$

Momentum $M = mv$ (correct)

Momentum $M = Fv$

In the context of momentum, what is the relationship between force and momentum?

Force is independent of momentum.

Force cancels out momentum entirely.

Momentum can exist without any force acting.

Force is equal to the rate of change of momentum. (correct)

For incompressible fluids, which factor remains constant in momentum calculations?

Density $ρ$ remains constant. (D) Signup and view all the answers

What does the control volume concept apply to in fluid mechanics?

A fixed section of fluid flow. (D) Signup and view all the answers

What is the significance of drawing a labeled control volume?

It simplifies equations for forces and energy. (B) Signup and view all the answers

During the application of a free jet striking a plate, what is assumed about the plate?

The plate has no friction with zero force. (D) Signup and view all the answers

In fluid mechanics, what determines the rate of change of momentum in a stream tube?

Fluid density and volume flow rate. (A) Signup and view all the answers

What is the formula for output power in the context of a flat plate?

Output power = $F_x v$ (A) Signup and view all the answers

How is the efficiency (η) calculated for a flat plate?

η = $\frac{O.P}{I.P}$ (B) Signup and view all the answers

To achieve maximum efficiency for a flat plate, which condition must be met?

V = 2v (D) Signup and view all the answers

What is the derived formula for the force exerted on a series of moving plates?

F_n = $\rho Q v_r$ (C) Signup and view all the answers

What is the relationship between the jet velocity (V) and the relative velocity (v_r) when dealing with a single moving curved plate?

v_r = V - v (B) Signup and view all the answers

What is the formula for input power (I.P.) in the context of a flat plate?

I.P. = $\rho Q \frac{V^2}{2}$ (C) Signup and view all the answers

When considering a fixed plate, how is the force in the x-direction defined?

F_x = $\rho Q (V - V \cos \theta)$ (C) Signup and view all the answers

In the context of a curved plate, what is the formula for the y-direction force (F_y)?

F_y = $\rho Q (0 - V \sin \theta)$ (D) Signup and view all the answers

What effect does a greater radius of bend have on flow resistance?

Reduces flow resistance (C) Signup and view all the answers

Which equation represents the force acting on the fluid in the x direction?

Fx = -P1A1 + P2A2cosθ + Q/g[v2cosθ - v1] (C) Signup and view all the answers

What happens to the weight W if the bend is horizontal?

W is not considered in calculations (B) Signup and view all the answers

Which of the following represents the total force required to hold the bend in place horizontally?

Fx = m(-V2 - V1) - P1A1 + P2A2 (C) Signup and view all the answers

Which equation relates to the vertical component of force on the fluid?

Fz = -P2A2sinθ - W + Q/g[v2sinθ - 0.0] (C) Signup and view all the answers

How is the total force FT calculated?

FT = √(Fx^2 + Fz^2) (C) Signup and view all the answers

When analyzing fluid forces, which of the following parameters does not directly affect the x direction's force?

Gravitational force (B) Signup and view all the answers

Which variable in the momentum equation represents the mass flow rate?

m (D) Signup and view all the answers

What is the correct expression for the force in the x-direction on a fixed plate?

Fx = ρQ[vin - vout] (C) Signup and view all the answers

What would be the value of F_y for a fixed plate with equal incoming and outgoing flow rates?

0 (B) Signup and view all the answers

How do you calculate the horizontal force required to hold a fixed plate in position when water is discharged?

By applying Bernoulli's equation between points A and B (B) Signup and view all the answers

What is the relative velocity at which water strikes a moving plate if the plate's velocity is v?

V - v (C) Signup and view all the answers

What is the horizontal force F calculated in the example if the tank discharges 0.4 m³/s and the velocity at point B is 12.3 m/s?

4.9 kN (B) Signup and view all the answers

What is the formula for the force in the x-direction for a curved plate?

Fx = ρQ[vr - vrcosθ]* (A) Signup and view all the answers

What is the maximum efficiency formula in the context of a curved plate?

ηmax = 0.5(1 - cosθ) (D) Signup and view all the answers

Which equation represents the work done per unit time for moving plates?

W.D/t = Fx = ρQ[V - v](1 - cosθ) (D) Signup and view all the answers

How is the head loss in sudden enlargement calculated?

hl = (*V1 - V2)2/(2g) (B) Signup and view all the answers

What is the force on a fluid due to adjacent bodies in sudden enlargement?

F = ρQ(vout - vin) (D) Signup and view all the answers

What indicates that a sharp bend in a flow results in separation?

Increased turbulence downstream (B) Signup and view all the answers

What does the variable C_c represent in the context of contraction losses?

Ratio of cross-sectional areas Ac to A2 (A) Signup and view all the answers

For curved plates, what does ρ represent?

Density of the fluid (A) Signup and view all the answers

In the context of losses, which formula represents the relationship for sudden contraction?

hl = (Ac/<A2 - 1) *V22/(2g) (A) Signup and view all the answers

Study Notes

Fluid Mechanics: Chapter Four - Finite Control Volume Analysis

This chapter focuses on applications of the momentum principle using finite control volume analysis.
Key concepts include the law of conservation of momentum, control volume concept,, applications, free jet strikes plate, sudden expansion and contraction, and bends.
The law of conservation of momentum states that a body in motion cannot gain or lose momentum unless an external force is applied. This law is equivalent to Newton's Second Law of Motion, where force is equal to the rate of change of momentum.
Control volume analysis involves analyzing fluid flow within a defined control volume, which allows for determining forces on the fluid from surrounding bodies and forces on the fluid from surrounding bodies.
Applications of the momentum principle include analysing free jet strikes plate, sudden expansion and contraction, and bends,
Assumed conditions for free jet strikes plate include a smooth, frictionless plate, no impact, and the water velocity remains the same after striking the plate.
A control volume concept is useful for analyzing flow, forces, and energy in a fixed section of fluid, simplifying flow analysis in pipes.
Application examples on flat plate include fixed and moving plates, and series of moving plates: calculations and formulas.
Applications on curved plates include fixed and moving plates, formulas and calculations.
Important formulas include those related to momentum (M = mv), rate of momentum (dM/dt), forces (F = pQv or related parameters) and control volumes (Q = a*V) where Q represents flow rate.
The calculation of required horizontal force to hold a plate in position based on Bernoulli's equation between points A and B, using flow rate data, and relevant variables are given as example.

Losses in Sudden Enlargement

To understand losses due to sudden enlargement, the control volume ABCD is used and the Bernoulli's equation is applied between specified points, representing a physical scenario.
An equation showing the relationship between the static pressures (P), velocities (V), density (ρ) of the fluid and gravity (g) is used.

Losses in Sudden Contraction

Losses are mainly due to the sudden change in channel areas between Ac and A2.
Relevant parameters for determining losses includes: velocities, area changes, losses in sudden enlargement, and coefficient of contraction is used. (k)

Bends

Sharp bends produce separation downstream of the bend, causing turbulence and flow resistance.
Increased radius (of the bend) decreases flow resistance.
Calculations are provided for vertical bends, including forces and pressures, for both horizontal (involving no vertical weight or elevation) and non-horizontal bends.
Flow rate calculations and other technical data are given for example solutions.

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Description

Explore the principles of finite control volume analysis in fluid mechanics through this quiz. Key concepts include the conservation of momentum, applications involving free jet strikes on plates, and the effects of sudden expansion and contraction. Test your understanding of how these principles apply in real-world scenarios.