The drag on an airplane wing in flight is known to be a function of the density of air
Show that the dimensionless drag,
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- For the flow of a viscous fluid, with the velocity V = f(x)g(y)h(z)i (where f, g, h are arbitrary functions), the following conditions are given: . The flow is adiabatic. • The quantities v = 2 and 3 = $ are constants. • The velocity circulation is conserved for the flow, irrespective of the values of vand 3. What is the general solution for the functions f, g, h?arrow_forwardA- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both speciesarrow_forwardConsider steady viscous flow through a small horizontal tube. For this type of flow, the pressure gradient along the tube, Δp ⁄ ΔL should be a function of the viscosity Y, the mean velocity V, and the diameter D. By dimensional analysis, derive a func- tional relationship relating these variables. Fluid mechanicsarrow_forward
- The power P required to drive a propeller is known to depend on the diameter of the propeller D, the density of fluid ρ, the speed of sound a, the angular velocity of the propeller ω, the freestream velocity V , and the viscosity of the fluid µ. (a) How many dimensionless groups characterize this problem? (b) If the effects of viscosity are neglected, and if the speed of sound is not an important variable, express the relationship between power and the other variables in nondimensional form. (c) A one-half scale model of a propeller is built, and it uses Pm horsepower when running at a speed ωm. If the full-scale propeller in the same fluid runs at ωm/2, what is its power consumption in terms of Pm if the functional dependence found in part (b) holds? What freestream velocity should be used for the model test?arrow_forwardMott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?arrow_forwardFor low-speed (laminar) steady flow through a circular pipe, as shown in Fig. P1.12, the velocity u varies with radius and takes the form u = B(rở - r?) where u is the fluid viscosity and Ap is the pressure drop from entrance to exit. What are the dimensions of the constant B? Pipe wall r=r и (г) r= 0 P1.12arrow_forward
- The kinematic viscosity of and specific gravity of a liquid are 3.5 x 10-4 m^2 /s and 0.79, respectively. What is the dynamic viscosity of the liquid in N-s/m^2?arrow_forwardA ship 350 m long moves in sea water whose density is 1030 kg/m3 . A 1:120 model of this ship is to be tested in a wind tunnel. The velocity of the wind tunnel around the model is 35 m/s and the resistance of the model is 65 N. Determine the velocity and also the resistance of the ship in sea water. The density of air is given as 1.24 kg/m3 . Take the kinematic viscosity of air and sea water as 0.012 stokes and 0.018 stokes respectively.arrow_forwardCOE0051 FLUID MECHANICS 2 PROPERTIES OF FLUIDS Section Break (Continuous)- 1. A 30x60 cm plate is pulled through the oil with viscosity of 0.05 kg/m-s. The distance between the parallel plates are 1.5 cm. If the plate is need to pull at the rate of 0.4 m/s, what is the force needed to attain this velocity? FIXED PLATE лиши 1.5 cm FIXED PLATE October 20, 2022 .5 cm 1.0 cm .4 m/sarrow_forward
- A seA A, soA A solid cylinder of diameter d, length and density p, falls due to gravity inside a pipe of diameter D. The clearance between the solid cylinder and the pipe is filled with a Newtonian fluid of density p and u. For this clearance fluid, the terminal velocity of the cylinder is determined to be V, assuming a linear velocity profile. However, if the clearance fluid was changed to a Newtonian fluid of density 2p and viscosity 2u, then for an assumed linear velocity profile, the terminal velocity of the cylinder was determined to be V,. From the results of these experiments, one may write that (A) V = V (C) 2 V= V (B) V=2 V, (D) V= 4 Varrow_forwardA block of mass m slides along a horizontal surface lubricated with a thick oil which providesa drag force proportional to the square root of velocity.F_d=-bv^1/2If v = v0 at t = 0, determine v as a function of timearrow_forwardThe property of a fluid called viscosity is related to its internal friction and resistance to being deformed. The viscosity of water, for instance, is less than that of molasses and honey, just as the viscosity of light motor oil is less than that of grease. A unit used in mechanical engineering to describe viscosity is called the poise, named after the physiologist Jean Louis Poiseuille, who performed early experiments in fluid mechanics. The unit is defined by 1 poise = 0.1 (N s)/m2. Show that 1 poise is also equivalent to 1 g/(cm · s). %3Darrow_forward
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