Newton's second law is the foundation for the differential equation of conservation of linear momentum (to be discussed in Chap. 9). In terms of the material acceleration following a fluid particle (Fig. P7-23), we write Newton's second law as follows:
Or, dividing both sides by the mass m of the fluid particle,
Write the primary dimensions of each additive term in the (second) equation, and verify that the equation is dimensionally homogeneous. Show all your work.
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Fluid Mechanics: Fundamentals and Applications
- Let's say that the semiempirical binding energy formula is Eb= aA-bA^2/3 - s(N-Z)^2/A -dZ^2/A^1/3 where a,b,s,d are constants. Imagine that you are in a different universe where there are 3 types of nucleons with spin equal to 1/2 and electric charges equal to +1, -1 and 0. Mass similar to that of a proton. Forces are similar to those of our universe. i) How do equations change for A and Z as a function of N+, N-, No and what is the semiempirical equation for the binding energy as a function of A, Z, and No? ii) At what Z and No do we have the maximum and minimum binding energy for every A? iii) When do we have stable nuclei under beta (β) decay? If "alpha particle" in this situation has N+ = N- = No = 2, what does apply for alpha (α) decay? iv) What does apply for nuclear fission and finally, how would life be in this situation?arrow_forwardIn fluid mechanics, which of the following are true: (a) Fluid mechanics is the branch of science concerned with stationary fluids (b) Fluids like water posses only potential energy (c) The field of fluid mechanics is infinite and endless (d) It is a branch of physics which concerns the study of liquids and the ways in which they interact with forces (e) It is a sience concerned with the response of fluids to forces exerted upon them, (f) the fluid which is in state of rest is called as static fluid and its study is called as statics.arrow_forwardEXAMPLE 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 50000arrow_forward
- Consider the following examples: 55 mph NE • 173 lb horizontal • 9.8067 m/s? down The above examples are quantities. scalar vectorarrow_forwardH.W: Two blocks connected by a cord passing over a small frictionless pulley rest on frictionless plane, as in fig. below, (a)which way will the system move? (b)what is the acceleration of the block (c)what is the tension in the Ans. (a) To left (b)0.65m/s (c)43.37N cord? N-100Neut N-50leut 30 330 1020arrow_forwardConsider steady, incompressible, two-dimensional flow due to a line source at the origin. Fluid is created at the origin and spreads out radially in all directions in the xy-plane. The net volume flow rate of created fluid per unit width is V·/L (into the page of Fig), where L is the width of the line source into the page in Fig Since mass must be conserved everywhere except at the origin (a singular point), the volume flow rate per unit width through a circle of any radius r must also be V·/L. If we (arbitrarily) specify stream function ? to be zero along the positive x-axis (? = 0), what is the value of ? along the positive y-axis (? = 90°)? What is the value of ? along the negative x-axis (? = 180°)?arrow_forward
- (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-ахisarrow_forwardd²u dy² pg where g is the acceleration due to gravity Harrow_forwardWhen a valve is opened, a certain fluid flows through the choke duct or valve (see figure), according to the relationship: V= V (1 + x/L) i Determine a) If the flow is stationary or transient. b) The acceleration (ax) of the fluid applying Euler's approach. c) The position of the particle as a function of time at x = 0 and t = 0. d) Determine the acceleration of the particle as a function of time.arrow_forward
- You are doing a problem that requires Reynold's Transport Theorem with Conservation of Mass. You carefully write the equation and then on the second line you write: 0 = v3 A3 - Svị dA1 + f vzdA2 What statements in the question or assumptions you make would lead you to this simplification? Mark all that apply. The flow is steady. Newtonian Fluid Incompressible fluid. Inviscid fluid. Inlets have uniform flow. Exits have uniform flow. Velocity is only in the x-direction.arrow_forwardThe wind flutter on the wing of a newly proposed jet fighter is given by the following 1st order differential equation: dy/dx = 2yx With the Boundary Condition: y(0) = 1 (remember this means that y = 1 when x = 0) Determine the vertical motion (y) in terms of the span (x) of the wing. The frequency of fluctuations of the wing at mach 2 is given by the non-homogenous 2nd order differential equation: y'' + 3y' - 10y = 100x With the boundary conditions: y(0) = 1 and y(1) = 0 (i.e., y = 1 when x = 0 and y = 0 when x = 1) By solving the homogenous form of this equation, complete the analysis and determine the amplitude (y) of vibration of the wing tip at mach 2. Critically evaluate wing flutter and fluctuation frequency amplitude determined by solving the two differential equations above.arrow_forward1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP|B² Vz = 2µL B a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B? v, = 2μL Problems 11 - 2B --– €. (a) 2B (b) Figure 1.3. Flow between parallel plates. b) Calculate the volumetric flow rate by using the velocity distributions given above. What is your conclusion? 2|A P|B³W Answer: b) For both cases Q = 3µLarrow_forward
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