Solve for the specific volume and specific weight in SI units and Dynamic Viscosity in Poise. The specific gravity of alcohol is 0.52 and its kinematics viscosity is equal to (your registration number/2 e.g., 4193/2) Centi Stokes
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- Evaluate the dimensionless groups hcD/k,UD/, and cp/k for water, n-butyl alcohol, mercury, hydrogen, air, and saturated steam at a temperature of 100C. Let D=1m,U=1m/sec, and hc=1W/m2K.The Archimedes number, Ar, used in the flow of stratifiedfluids, is a dimensionless combination of gravity g , densitydifference Δ ρ , fluid width L , and viscosity μ . Find theform of this number if it is proportional to g .The Ekman number, Ek, arises in geophysical fluiddynamics. It is a dimensionless parameter combining seawaterdensity ρ , a characteristic length L , seawaterviscosity μ , and the Coriolis frequency Ω sin φ , where Ωis the rotation rate of the earth and φ is the latitude angle.Determine the correct form of Ek if the viscosity is in thenumerator.
- The quantities viscosity µ, velocity V, and surface tension Y may be combined into a dimensionless group. Find the combination which is proportional to µ. This group has a customary name, which begins with C. Can you guess its name?Consider the pressure Drop depends on : characterstic lugth I density gravity g speed of sound с angular velocity w Surface tension 6 Velardy of fluid V Viscosity of M write an an expression of the pressu drop ?Books on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid can be combinedwith a characteristic velocity U to form an important dimensionlessparameter. ( a ) Verify that this is so. ( b ) Evaluatethis parameter for water at 20°C and a velocity of3.5 cm/s. Note: You get extra credit if you know the nameof this parameter.
- Aeronautical engineers measure the pitching moment M0of a wing and then write it in the following form for use inother cases:M0 =βV2 AC ρ where V is the wing velocity, A the wing area, C the wingchord length, and ρ the air density. What are the dimensionsof the coeffi cient β ?The surface tensions of mercury and water at 60 degrees Celcius are 0.47N/m and 0.0662 N/m, respectively. What capillary height changes will occur in these two fluids when they are in contact with air in a glass tube of radius 0.30mm? Use θ = 130° for mercury, and 0° for water; y = 132.3 kN/m3 for mercury and 9.650 kN/m3 for water. Provide the given along with its solution. (Please write legibly, I did not understand the first solution.)Consider the pressure Drop depends on: @ characterstic lugth I 2 density ℗ gravity g speed of sound с angular velocity w surface tension Velocity of fluid V Viscosity of fluid write an expression of the pressu drop ?
- When disturbed, a floating buoy will bob up and down atfrequency f . Assume that this frequency varies with buoymass m , waterline diameter d , and the specific weight γ ofthe liquid. ( a ) Express this as a dimensionless function. ( b )If d and γ are constant and the buoy mass is halved, howwill the frequency change?The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.Derive two dimensionless parameters for the shear stress at the pipe wall when an incompressible fluid flows through a pipe under pressure. In the dimensional analysis, use the following significant parameters: pipe diameter, flow velocity, viscosity of the fluid and density of the fluid. Solve the problem on white A4 size paper. Show all the calculation steps.