Flow Around a Bend in a Rectangular Duct Partial Report

PLS SHOW ME FULL STEPS SIR PLS ANSWER WITHIN 30 MIN SIR SUBJECT (FLUID MECH 2) use setting 2

How do you get from equation 3.1.1 to 3.1.5? I understand that yoy mutiply both sides by Ui, but I'm confused on the math that is done to bring Ui into the partial derivative. Please show all intermediate steps.

Fluid Mechanics Problem:  Assume all fluids are 20oC.

Problem 4: The power P developed by a wind turbine is a function of diameter D, air density p, wind speed V, and rotational rate @. Viscous effect is negligible. (4a) Rewrite the above relationship in a dimensionless form; (4b) In a wind tunnel, a small model with a diameter of 90cm, rotating at 1200 RPM (revolution per minute), delivered 200 watts when the wind speed is 12m/s. The data are to be used for a prototype of diameter of 50m and wind speed of 8 m/s. For dynamic similarity, what will be (i) the rotational speed of the prototype turbine? (ii) the power delivered by the prototype turbine? Assume air has sea-level density.

> | E9 docs.google.com/form تبديل الحساب Questions 7 نقاط Q1/ The power of 6-blade flat blade turbine agitator in a tank is a function of diameter of impeller, number of rotations of the impeller per unit time, viscosity and density of liquid. From a dimensional analysis, obtain a relation between the power and the four variables. 3. صفحة 2 من

PLEASE BOX YOUR ANSWERS Problem 2 In an experiment conducted in a laboratory, the surface tension (Y) acting on a rotating square plate in a viscous fluid is a function of the external torque (t), plate length (a), area moment of inertia of plate (I), specific weight of the fluid (Y) and angular displacement of the plate (0). Using Buckingham-Pi theorem, find a suitable set of pi terms (in M, L and T primary dimensions). Your final answer should be written in proper functional form. Refer Table 5.1/ page-296 for secondary dimension of the variables.

#4 1.11 For a small particle of styrofoam (1 lbm/ft) (spherical, with diameter d = 0.3 mm) falling in standard air at speed V, the drag is given by FD-3mVd, where is the air viscosity. Find the maximum speed starting from rest, and the time it takes to reach 95 percent of this speed. Plot the speed as a function of time. s) Answer: (Vmax=0.0435",t=0.0133 S

You are employed as a mechanical engineer within an unnamed research center, specializing in the development of innovative air conditioning systems. Your division is tasked with providing computer-based modeling and design solutions using computational fluid dynamics through ANSYS software. Your primary responsibilities involve the analysis of horizontal channel dynamics to meet specific criteria. Under the guidance of your immediate supervisor, you have been assigned unique responsibilities within an ongoing project. As a member of the research team, your role includes constructing an appropriate model and executing a sequence of simulation iterations to explore and enhance channel performance. Figure 1 provides a visualization of the horizontal channel under consideration. Consider 2D, incompressible, steady flow in a horizontal channel at a Reynolds number of 150. The schematic below illustrates the channel flow, not drawn to scale. For simplicity, neglect gravity. The channel's…

[1] Consider steady flow of air through the diffuser portion of a wind tunnel. Along the centerline of the diffuser, the air speed decreases from uentrance to ut as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, Dee x=0 to x=L.

Fluid Mechanics Problem

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The thrust F of a Free propeller, either aircraft of marine, depends upon density ρ, the rotation rate n in r/s, the diameter D, and the forward velocity V. Viscous effects are slight and neglected here. Tests of a 25-cm-diameter model aircraft propeller, in a sea-level wind tunnel, yield the following thrust data at a velocity of 20 m/s : Rotation Rate, r/min____4800____6000____8000 Measured thrust, N____6.1____19____47 Use the dimensionless data to predict the thrust, in Newtons, of a similar 1.6-m-diameter prototype propeller when rotating at 3800 r/min and flying at 225 mi/h at 4000-m standard altitude.

(b) One form of fluid movement is rotation and deform angularly. Figure Q1(b) shows the rotation and angular deformation caused by velocity variation about z-axis. Based on Table 1 and setting given to you, derive an equation of rotation. ди Sy St ây > B' ĉu B B ôy dy A' ↑ Sa v+. ôx A ôx Figure Q1(b) : Rotation and Angular Deformation Table 1: Axis of Rotation Setting Axis of Rotation 2 у-ахis

Q.10. To predict the drag on an aircraft at a flight speed of 150 m/s, where the condition of air is such that the local speed of sound is 310 m/s, a pressurized low temperature tunnel is used. Density, viscosity and local sonic velocity at tunnel condition are 7.5 kg/m³, 1.22 x 105 Ns/m² and 290 m/s. Determine the flow velocity and the scale of the model. Assume full dynamic similarity should be maintained. Density and viscosity at the operating conditions are 1.2 kg/m³ and 1.8 x 105 Ns/m².

The power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate Ohm, the density rho, and viscosity mu of the fluid. Rewrite this as a dimensionless relationship

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One of the conditions in using the Bernoulli equation is the requirement of inviscid flow. However there is no fluid with zero viscosity in the world except some peculiar fluid at very low temperature. Bernoulli equation or inviscid flow theory is still a very important branch of fluid dynamics for the following reasons: (i) (ii) There is wide region of flow where the velocity gradient is zero and so the viscous effect does not manifest itself, such as in external flow past an un- stalled aerofoil. The conservation of useful energy allows the conversion of kinetic and potential energy to pressure and hence pressure force acting normal to the control volume or system boundary even though the tangential friction stress is absent. It allows the estimation of losses in internal pipe flow. (A) (i) and (ii) (B) (i) and (iii) (ii) and (iii) All of the above (C) (D)

A jet engine on a test stand directs a stream of hot exhaust gasses against a vemcal wall. All of the exhaust gas leaving the wall after impact is in the y-z plane (ie no "x" direction velocity). The mass rate is 200 kg/s and the velocity is 400 m/s. (Note that the density and viscosity are not relevant) What is the force on the wall (include direction)?

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(b) A wind-tunnel experiment is performed on a small 1:5 linear-scale model of a car, in order to assess the drag force F on a new full-size car design. A dimensionless "drag coefficient" Ca is defined by C, =- pu'A where A is the maximum cross-sectional area of the car in the flow. With the model car, a force of 3 N was recorded at a flow velocity u of 6 m s. Assuming that flow conditions are comparable (i.e., at the same Reynolds number), calculate the expected drag force for the full-sized car when the flow velocity past it is 31 m s (equivalent to 70 miles per hour). [The density of air p= 1.2 kg m.]

EXAMPLE Leaking Tank. Outflow of Water Through a Hole (Torricelli's Law) This is another prototype engineering problem that leads to an ODE. It concerns the outflow of water from a cylindrical tank with a hole at the bottom. You are asked to find the height of the water in the tank at any time if the tank has diameter 2 m, the hole has diameter 1 cm, and the initial height of the water when the hole is opened is 2.25 m. When will the tank be empty? 2.20 M Water level asime Outiine walls 200 200 30t .00- 50- D 10000 30000 tebe Revelion 50000

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Particles in liquids achieve terminal speed very quickly. One can measure the time it takes for a particle to fall a certain distance and then calculate the constant B. Suppose a steel ball bearing (mass=0.86 grams) is dropped in a container of motor oil. It takes 12 s to fall 0.60 m. (a) Estimate the terminal speed, Viem, assuming the ball bearing reaches terminal speed almost immediately. (answer: Vterm 0.050 m/s) (b) Calculate B. (answer: 0.17 kg/s) (e) What is the speed of the ball bearing 11 ms after it is dropped? (answer: 0.044 m/s)

8.1. An airplane wing of 3 m chord length moves through still air at 15°C and 101.3 kPa at a speed of 320 km/h. A !:20 scale model of this wing is placed in a wind tunnel, and dynamic similarity between model and prototype is desired. (a) What velocity is necessary in a tunnel where the air has the same pressure and temperature as that in flight? (b) What velocity is necessary in a variable-density wind tunnel where absolute pressure is 1 400 kPa and temperature is 15°C? (c) At what speed must the model move through water (15°C) for dynamic similarity?

A paramecium is an elongated unicellular organism with approximately 50 μmin diameters and 150 μmin lengths. It swims through water by whip-like movements of cilia, small hairs on the outside of its body. Because it moves "head first" through the water, drag is determined primarily by its diameter and only secondarily by its length, so it's reasonable to model the paramecium as a 70-μm diameter sphere. A paramecium uses 2.0 PW of locomotive power to propel itself through 20∘C water, where 1 pW = 1 picowatt = 10−12W.   What is its swimming speed in μm/s? Express your answer in micrometers per second.

Computational fluid dynamics

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As we learned, Bernoulli's equation is not to be used in many situations. Let's say you are examining changes between two points in a flow. Which ONE of these scenarios could you appropriately use Bernoulli's equation on? O A turbine is situated between the two points There are large changes in kinetic energy between the two points The mass flow rate between the two points changes with time There are large changes in density between the two points There are large viscous losses between the two points QUESTION 10 A 12 cm diameter jet of air strikes a plate positioned normal to the flow, with all air deflected away parallel to the plate. If the air flows at a speed of 20 m/s, what is the force needed to held the plate in place? Do not use a linear momentum correction factor. O 0.272 N 10.9 N 4510 N 5.45 N 0.340 N

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