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- 6. The velocity in a 2-cm diameter pipe is 20 m/s. If the pipe enlarges to 5-cm in diameter, the velocity, in m/s, will be:a. 8.0b. 6.4c. 3.2d. 2.0air flow steadily through a along pipe with a speed of u=50+0.5x,where x is the distance along the pipe in m,and u is in m/s.Due to heat transfer into to the pipe,air temperature,T,witin the pipe is T=300+9x C.Determine the rate of change of the temperature of air particles as they flow past the section at x=5mUsing Newton's second law, the movement of a body in a viscous fluid can be modeled. For this case it will be a one-dimensional movement. ec.1) F -FR = ma F: Force applied to the body. FR: Resistance that opposes the fluid to the movement. m: body mass a: body acceleration For a sphere with initial radius R0 = 1 meter and density 8960 kg/m^3 to which a constant force of 3 Kilo Newtons is applied, it is requested: Using Euler's method, find the velocity as a function of time for the first 5 seconds of movement, considering that v(0) = 10 m/s. Use a 1 second step. For this case use: ec.2) FR = 210Rv R: Radius of the sphere. v: velocity Where, in addition, the sphere disintegrates as time passes in this fluid, so its radius is given by the following function: ec.3) R = R0*e^(-t/250)
- Two endlessly long flat plates, separated by 3 inches in distance but with a thickness of 5 inches, each transport alcohol (5 m/s, 1 Pa·s, S.G. 0.89 (ref. water at 4 degrees Celsius) to a given location with a specific velocity. Prove that the Reynold's number of the following problem is a value approximately around 90-100.A gun is on the same horizontal level as a target 484 meters away. A bullet is fired from the gun with a muzzle velocity of 154m/s. At what angle of elecation should the muzzle of the gun be set in order to ensure the bullet hits the target? Hint: You may use the formulas for the horixzontal x(t) and vertical y(t) displacement of the particle: x(t) = ucos(α)t, y(t) - usin(α)t - ½gt2 , g = 10m/sec2.In an oil pool, a small steel ball is released from the surface (y=0) without initial velocity. The strength of the resistance force exerted by the oil against the movement of the ball is directly proportional to the speed of the ball (Fd = k*V , k: constant). Neglect the buoyant force exerted by the oil. (m = 0.2kg, k = 0.843550 kg/s, g = 9.81 m/s^2). a-) What is the limit speed of ball ( Vlim)? b-) What is the time it takes for the speed of the ball to reach 99% of the limit speed after it is released from the surface? c-) What is the depth at which the ball's velocity reaches 99% of the limit velocity after it is released from the surface?
- The calculation of power from moving fluid has the following parameters: Volume Flow rate = 10 +/- 0.154 m^3/sDensity of water = 1025 kg/m^3 Head of water = 150m +/- 10cmDetermine the range of values the power will be calculated.Fluid Mechanics Question An incompressible fluid flows in the converged nozzle provided in the figure. nozzle area -> A=Ao*(1-b*x) entry speed -> V=Vo*(0.5+0.5*cos(w*t)) Vo:20m/s Ao=1.5 m2 L=13m b=0.2/22 W=0.16rad/s Find the acceleration in the nozzle center as a function of time * (to multiplication) / (to divide)Water is flowing in a 3-cm-diameter garden hose at a rate of 25 L/min. A 20-cm nozzle is attached to the hose which decreases the diameter to 1.2 cm. The magnitude of the acceleration of a fluid particle moving down the centerline of the nozzle is (a) 9.81 m/s2 (b) 17.3 m/s2 (c) 28.6 m/s2 (d ) 33.1 m/s2 (e) 42.4 m/s2
- Liquid biofuel (density= 789 kg/m3) is being pumped from a storage tank through a pipe with 1-inch innerdiameter (ID). The fuel is being pumped at a rate of 3.00 gallons per minute. In this process, what is thekinetic energy transport rate (Ėk) in units of horsepower (hp) and ft•lbf/sec.Unless stated otherwise take:Patm = 10^5, P(water) = 1000 kg/m^3 ; P(air) = 1.2 kg/m^3 ; g = 9.8m/s^2gage pressure Pg = P - PatmUnless specified otherwise assume uniform velocity profiles in duct locations.The Bernoulli eq’n (BE), P + ½ρV2 + ρgz = constant In this formulation the scalar variable z is the vertical height measured opposite the direction of g (z is always taken up independent of your coordinate system; pgz is potential energy)This BE is only valid along a streamline in steady state flow, when viscous friction effects can be ignored, called “ideal” fluid motion, and the density is assumed to be constantthe differential radial component of –?P + ρg = ρawith the centripetal acceleration , ar = - V^2/r , to get dp/dr = ρgr + ρV^2/rThe Bernoulli eq’n is often divided through by the constant ρg ≡ γ so that each term has units of length, a height or “head” : (P/ ρg) + (V2/2g) + (z) = constant. Q = VA = flow rate = constant, as a second eq’n to solve for an unknown velocity. the…Show complete solution: A vessel of volume V, with a constant cross-sectional area of A and a height of H, is initially (t = 0) filled with a fluid having a density of ρ. At a certain time (t > 0), a drain was opened at the bottom of the vessel for the fluid to flow through by gravity. The velocity coming out of the drain is expressed as vout = C0 (gh)1/2 where C0 is a constant, g is the acceleration due to gravity, and h is the height of the fluid inside the tank. Develop an equation for the height h as a function of time t.