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5. Problem 4-175* (note: the 'continuity equation' is the conservation of mass principle. M = Mo...
Using the fundamental principle of conservation of mass, derive the continuity equation in 1D Saint-Venant equation.
Using the fundamental principle of conservation of mass, derive the continuity equation in 1D Saint-Venant equation.
Three fundamental conservation equations will be practiced in this problem. Attached figure shows the smooth merging of...
Three fundamental conservation equations will be practiced in this problem. Attached figure shows the smooth merging of two free jets of SAE30 oil in open air on a horizontal plane. Assume that, without any dispersion, they form a homogeneous jet a) Write the momentum principle in x and y directions and manipulate the two equations to derive a relationship for angle a in terms of given information: Vi=6 m/s, V2=4 m/s, di-0.1 m, d 0.12 m and 0 45°. Calculate...
In addition, derive the "wave equation" for an incompressible fluid. Use the continuity equation and the...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
Momentum Theory Use one-dimensional conservation of momentum together with conservation of mass (continuity) and energy (Bernoulli’s...
Momentum Theory Use one-dimensional conservation of momentum together with conservation of mass (continuity) and energy (Bernoulli’s equation = mechanical energy) to derive the power an ideal, frictionless wind turbine with an infinite number of blades, uniform thrust over the rotor area and a non-rotating wake can extract from the wind. Formulate the derivation in terms of the fractional decrease in wind velocity between the velocity far upstream and at the turbine rotor, ? = (? − ?)/?, also called “axial...
Problem 4 Write the equation of motion of the system shown in Figure 3 using either...
Problem 4 Write the equation of motion of the system shown in Figure 3 using either Newton's law or the principle of conservation of energy. Pulley, mass moment of inertia J. x(1) Figure 3
PROBLEM 5 Starting with the integral equation of motion, Ot derive the differential form of the e...
PROBLEM 5 Starting with the integral equation of motion, Ot derive the differential form of the equation. Hint: To do this, look at how we derived the differential form of the mass continuity equation. There are parallels, although thisis more complicated. Note that youil ave to apply the gradien identt. fHp di -
5. One of the simplest ways to recapture the Reynolds stress is to time-average the conservation...
5. One of the simplest ways to recapture the Reynolds stress is to time-average the conservation form of the axial momentum equation in Cartesian coordinates. (a) Start by expanding (xial momentum in conservation form) Then using the continuity equation, show that the result is identical to the traditional form: +1, (steady, incompressible, axial momentum form) (b) By substituting the Reynolds decomposed variables, u +,p-p+p', into the conservation form, time-averaging, cancelling terms that average out, and assuming that streamwise variations in...
CHE 3315 FLUID MECHANICS PROBLEM SHEET 5: MASS CONSERVATION AND FLOW RATE 1. Determine the mass...
CHE 3315 FLUID MECHANICS PROBLEM SHEET 5: MASS CONSERVATION AND FLOW RATE 1. Determine the mass flow rate of air having a temperature of 20C and gauge pressure 80 kPa as it flows through a circular duct 400 mm in diameter with an average velocity of 3 m/s. The gas specific constant R 286.9 JK /kg 2. Determine the average velocity of the steady flow at one outlet of a T- junction if the inlet flow speed is 6 m/s...
(SULIT) QUESTION 2 (20 MARKS) a. Describe the concepts of "Conservation of Mass" and "Conservation of...
(SULIT) QUESTION 2 (20 MARKS) a. Describe the concepts of "Conservation of Mass" and "Conservation of Energy" used in connection with flows in pipes. Sketch an appropriate diagram to support your arguments. (CO2: PO2 - 6 Marks) b. In a water supply system, water flows in from pipes 1 and 2 and goes out from pipes 3 and 4 as shown in Fiqure Q2 (b). If all the pipes have the same diameter, explain the flow velocities in each pipe...
In this problem, you apply the Continuity Equation in 3 ways. In this problem, you apply...
In this problem, you apply the Continuity Equation in 3
ways.
In this problem, you apply the Continuity Equation in 3 ways. Artery Region 2 Region 1 Keep 3 decimal places. (a) As shown in the above figure, a major artery (region 1) with a cross-sectional area of 1.00 cm2 branches into (region 2) 18 smaller arteries, each with an average cross-sectional area of 0.48 cm2. Find the ratio of v,/ V, (in decimal), where v, is the average speed...
Three fundamental conservation equations will be practiced in this problem. Attached figure shows the smooth merging of two free jets of SAE30 oil in open air on a horizontal plane. Assume that, without any dispersion, they form a homogeneous jet a) Write the momentum principle in x and y directions and manipulate the two equations to derive a relationship for angle a in terms of given information: Vi=6 m/s, V2=4 m/s, di-0.1 m, d 0.12 m and 0 45°. Calculate...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
Problem 4 Write the equation of motion of the system shown in Figure 3 using either Newton's law or the principle of conservation of energy. Pulley, mass moment of inertia J. x(1) Figure 3
PROBLEM 5 Starting with the integral equation of motion, Ot derive the differential form of the equation. Hint: To do this, look at how we derived the differential form of the mass continuity equation. There are parallels, although thisis more complicated. Note that youil ave to apply the gradien identt. fHp di -
5. One of the simplest ways to recapture the Reynolds stress is to time-average the conservation form of the axial momentum equation in Cartesian coordinates. (a) Start by expanding (xial momentum in conservation form) Then using the continuity equation, show that the result is identical to the traditional form: +1, (steady, incompressible, axial momentum form) (b) By substituting the Reynolds decomposed variables, u +,p-p+p', into the conservation form, time-averaging, cancelling terms that average out, and assuming that streamwise variations in...
CHE 3315 FLUID MECHANICS PROBLEM SHEET 5: MASS CONSERVATION AND FLOW RATE 1. Determine the mass flow rate of air having a temperature of 20C and gauge pressure 80 kPa as it flows through a circular duct 400 mm in diameter with an average velocity of 3 m/s. The gas specific constant R 286.9 JK /kg 2. Determine the average velocity of the steady flow at one outlet of a T- junction if the inlet flow speed is 6 m/s...
(SULIT) QUESTION 2 (20 MARKS) a. Describe the concepts of "Conservation of Mass" and "Conservation of Energy" used in connection with flows in pipes. Sketch an appropriate diagram to support your arguments. (CO2: PO2 - 6 Marks) b. In a water supply system, water flows in from pipes 1 and 2 and goes out from pipes 3 and 4 as shown in Fiqure Q2 (b). If all the pipes have the same diameter, explain the flow velocities in each pipe...
In this problem, you apply the Continuity Equation in 3
ways.
In this problem, you apply the Continuity Equation in 3 ways. Artery Region 2 Region 1 Keep 3 decimal places. (a) As shown in the above figure, a major artery (region 1) with a cross-sectional area of 1.00 cm2 branches into (region 2) 18 smaller arteries, each with an average cross-sectional area of 0.48 cm2. Find the ratio of v,/ V, (in decimal), where v, is the average speed...
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After watching the lectures I am still having a hard time
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H0:μ=56.9
H1:μ<56.9
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