Rep Rev MecFluidosProblemasMarzo2008

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COLEGIO DE INGENIEROS Y AGRIMENSORES DE PUERTO RICO URB. ROOSEVELT, HATO REY, P. R.

REPASO DE REVALIDA FUNDAMENTAL

PARA INGENIEROS

8 DE MARZO DE 2008 – Hato Rey

15 DE MARZO DE 2008 - Bayamón

PROBLEMAS - MECANICA DE LOS FLUIDOS

MIGUEL A. CRUZ AROCHO, BSCE, MSCE, MSEnvE, PE, RPA CATEDRATICO DPTO CIENCIAS DE INGENIERIA Y MATERIALES

UNIVERSIDAD DE PUERTO RICO - MAYAGUEZ

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DIVISIONES DE LA MECANICA (ENGINEERING SCIENCES)

1. MECANICA DE CUERPOS RIGIDOS a) Estática b) Dinámica (Cinemática, Cinética)

2. MECANICA DE CUERPOS DEFORMABLES a) Resistencia de Materiales I y II

3. ELEMENTOS DE MATERIALES DE INGENIERIA

4. MECANICA DE LOS FLUIDOS

a) Hidrostática

b) Hidrodinámica (líquidos y gases a baja velocidad)

c) Dinámica de gases (velocidad alta)

d) Aerodinámica (aviones y cohetes)

e) Otras áreas (base para otros campos)

1. Meteorología 5. Combustión 2. Oceanografía 6. Acústica 3. Astronomía 7. Biofluidos 4. Propulsión 8. Física de partículas

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REPASO PARA LA REVALIDA FUNDAMENTALMECANICA DE FLUIDOS

Mecánica de Fluidos - rama de la mecánica aplicada que tiene que ver con el estudio de los fluidos en movimiento o reposo y de sus efectos sobre los contornos.

Fluido - Es una sustancia que se deforma continuamente ante la presencia de un esfuerzo cortante.

Fluidos: Líquidos y Gases

Líquidos: Agua, Aceite, Mercurio, Gasolina, Alcohol

Gases: Aire, Helio, Hidrógeno, Vapor

Casos límite: Asfalto, Coloide, Fluidos multifases

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FLUID PROPERTIES

1 Density 2 Specific Volume3 Specific Gravity4 Specific Weight5 Mole Fraction6 Absolute Viscosity 7 Kinematic Viscosity8 Vapor Pressure9 Surface Tension10 Capillary Action11 Compressibility 12 Bulk Modulus13 Speed of Sound

FLUID STATICS

1 Pressure-Measuring Devices 2 Manometers 3 Hydrostatic Pressure4 Pressure on a Horizontal Plane5 Pressure on a Vertical Plane 6 Pressure on an Inclined Plane7 Forces on Curved Surfaces 8 Torque on a Gate9 Hydrostatic Forces on a Dam 10 Pressure due to Several Liquids 11 Buoyancy 12 Stability of Floating Objects

FLUID FLOW PARAMETERS

1 KineticEnergy 2 Potential Energy 3 Pressure Energy4 Bernoulli Equation5 PitotTube 6 Hydraulic Radius7 LaminarFlow 8 Turbulent Flow9 Critical Flow 10 Velocity Distribution11 Energy Grade Line12 Specific Energy

FLUID DYNAMICS

1 Conservation of Mass2 Head Loss Due to Friction3 Relative Roughness4 Friction Factor5 Loss Due to Friction: Laminar Flow6 Loss Due to Friction: Turbulent Flow7 Minor Losses 8 Bernoulli Equation9 Energy and Hydraulic Grade Lines10 Discharge from Tanks11 Series Pipe Systems

FLUID DYNAMICS (cont.)

12 Parallel Pipe Systems13 Flow Measuring Devices14 Pitot-Static Gage15 Venturi Meter16 Orifice Meter17 Flow Nozzle 18 Impulse-Momentum Principle19 Jet Impact on Flat Plates20 Terminal Velocity21 Similarity

HYDRAULIC MACHINES

1 Hydraulic Machines2 Types of Pumps 3 Pumping Power4 Pumping Efficiency. 5 Specific Speed6 Cavitation 7 Net Positive Suction Head8 Suction Specific Speed9 Pump Performance Curves10 Pumps in Parallel; in Series11 Types of Turbines

OPEN CHANNEL FLOW

1 Open Channel Flow2 Uniform Flow 3 Manning Equation 4 Normal depth 5 Friction Losses 6 Flow in Circular Sections 7 Triangular Weirs8 Trapezoidal Weirs9 Proportional Weirs10 Specific Energy Diagram11 Critical Flow in Rectangular Channels12 The Froude Number13 Hydraulic Jump and Drop

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LISTA POR ORDEN CRONOLOGICO SEGUN FECHA DE MUERTE DE ALGUNOS HOMBRES CELEBRES CON SUS APORTACIONES A LA

MECANICA DE FLUIDOS Y A LA HIDRAULICA

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Sesión de la Tarde

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FLUID MECHANICS

PROBLEMAS DE LA SESION DE LA MAÑANA

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FLUID MECHANICS


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FLUID MECHANICS PROBLEMAS DE LA SESION DE LA MAÑANA

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FLUID MECHANICS PROBLEMAS DE LA SESION DE LA MAÑANA

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FLUID MECHANICS


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FLUID MECHANICS PROBLEMAS DE LA SESION DE LA TARDE

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Sistema de Agua con Bomba y Turbina

FLUID MECHANICS – Afternoon Session

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Continuación del Problema de un Sistema de Agua con Bomba y Turbina

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Envase que Contiene Aceite y Agua

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1. The pressure on the bottom surface of the vat is most nearly

(A) 0.910 psi (6.27 kPa)(8) 1.11 psi (7.65 kPa)(C) 1.17 psi (8.07 kPa)(D) 1.30 psi (8.96 k Pa)(E) 1.85 psi (12.8 kPa)

2. The block is 6.0 inches (150 millimeters) deep and it floats with its upper surface 2.0 inches above the oil surface. The specific gravity of the block is most nearly

(A) 0.567 (B) 0.661 (C) 0.702 (D) 0.758 (E) 0.813

3. The ball is suspended with 40 percent of Itsvolume above the oil-water Interface. Thedensity of the ball is most nearly

(A) 55.l lbl/ ft3 (883 kg/ m3)(B) 56.7 lbl/ ft3 (908 kat ma)(C) 57.3 lbl/ ft3 (918 klima)(D) 58.7 lbl/ ft3 (940 kal ma)(E) 60.2 lb/ ft3 (964 kal m3)

4. Disregarding the presence of the stone, block and ball, the total weight of the liquid in the vat is most nearly

(A) 2,440 Ib (10.9 kN)(B) 2,680 Ib (11.9 kN)(C) 2,750 Ib (12.2 kN)(D) 2,820 Ib (12.5 kN)(E) 2,930 lb (13.0 kN)

5. The net force of the oil and water on the bottom of the vat is most nearly

(A) 2020 lb (9.00 kN)(B) 2280 lb (10.1 kN)(C) 2320 lb (10.3 kN)(D) 2500 lb (11.1 kN) (E) 2640 lb (11.7 kN)

Continuación del Problema del Envase con Aceite y Agua

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Figure P2.23

Prob. 2.23

Determine the water pressure in the pipe. The manomenter is open to the atmosphere.

Solution

Pa

hhpp wwxxatmw

8020

1.098103.0300000

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Prob. 2.26

Calculate the manomenter reading H.

SolutionFigure P2.26

kPaHkPa oHgw 1630.020.040

kPaSSHkPa wowHgw 1630.020.040

cmm

kPaH

43.171743.081.910006.13

)92.030.020.0(81.91000)1640(

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Figure P2.50

Problem 2.50

Determine the force P needed to hold the 4 m wide gate in the position shown in the figure at right.

778.75.720

54121

5.7

117710177.12069810

3

6

yA

Iyy

kNNAhF

p

Force of the water on the gate and its line of action Moment about the hinge

kNP

P

M hinge

5235

1177222.21177)778.710(5

0

26Figure P2.59

Problem 2.59

The pressure distribution over the base of a concrete (S=2.4) dam varies linearly , as shown in the figure, producing an uplift. Will the dam topple over ? (Hint: sum moments of all forces about the bottom, right-hand corner) Use: a) H=45 m, b) H=60 m

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Problems 1-4 are based on tile following information and illustration.

Water at 100C is pumped through smooth steel pipes from tank 1 to tank 2. The discharge rate is 0.1 m3/min. The kinematic viscosity of water at 100C is 1.31 x 10-6 m2 /s.

1. What is the ratio of the water velocity in the 3 cm pipe to the velocity in the 6 cm pipe?

(A) 1:1 (B) 2:1 (C) 4:1 (D) 8:1 2. What is the total friction head loss in the pipes?

(A) 4.7 m(B) 5.3 m (C) 9.6 m (D) 11 m

3. What head does the pump add?

(A) 10 m (B) 15 m (C) 25 m (D) 30 m

4. What is the pump's brake power?

(A) 32 W (B) 250 W (C) 310 W (D) 19 kW

Fluids Mechanics Exam Review Problems

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(A) 1.0 kPa (B) 13 kPa vacuum (C) 39 kPa vacuum (D) 78 kPa

7. A pressure vessel with an internal pressure, p is connected to the simple U-tube open to atmosphere as shown. A 10 cm deflection of mercury is observed. The density of mercury is 13.6 Mg/m3. What is the pressure, p, if the atmospheric pressure is 101 kPa?

8. Fluid flows at 5 m/s in a 5 cm diameter pipe section. The section is connected to a 10 cm diameter section. At what velocity does the fluid flow in the 10 cm section?

(A) 1.00 m/s(B) 1.25 m/s (C) 2.50 m/s (D) 10.0 m/s

9. A venturi meter installed horizontally is used to measure the flow of water in a pipe. The area ratio, A2/A1 , of the meter is 0.5, and the velocity through the throat of the meter is 3 m/s. What is the pressure differential across the venturi meter?

(A) 1.5 kPa (B) 2.3 kPa (C) 3.5 kPa (D) 6.8 kPa

6. How does the Reynolds number of a 1/15 scale model relate to the Reynolds number of the prototype:

(A) They are both equal (B) The Reynolds number of the model is 15 times lower. (C) The Reynolds number of the prototype is 15 times lower. (D) The Reynolds number of the model is a function of the velocity ratio.

5. The tank shown is filled with water. The gate is mounted on frictionless bearings on the hinged edge. What is the resultant force (per meter of wall width) required to keep the gate closed?

(A) 19.6 kN (B) 27.6 kN (C) 29.4 kN (D) 33.1 kN


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10. The 8 cm by 12 cm rectangular flume shown is filled to three-quarters of its height. What is the hydraulic radius of the flow?

(A) 1.5 cm (B) 2.5 cm (C) 3.0 cm (D) 5.0 cm

11. Water is flowing at the rate of 0.01 m3 /s in the vertical pipe system shown. What is the pressure at point 2 ?

(A) 49.4 kPa (B) 111 kPa (C) 375 kPa (D) 675 kPa


12. A waterfall has a total fall of 15 m and a flow rate of 2 m3 /s. What theoretical power is available?

(A) 294 kW (B) 375 kW(C) 439 kW (D) 750 kW

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Figure E2.6

Example 2.6

Find the location of the resultant force F of the water on the triangular gate and the force P necessary to hold the gate in the position shown in the figure.

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Example 2.7

Calculate the force P necessary to hold the 4 m wide gate in the position shown in the figure. Neglect the weight of the gate.

Rep Rev MecFluidosProblemasMarzo2008

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