The lift of a wing, Fit, is a function of wingspan, W, chord length, H, surrounding air density, p, and viscosity, µ, and velocity, V. Using p, V, and W as repeating variables, express this relationship in dimensionless form.

The lift of a wing, Fit, is a function of wingspan, W, chord length, H, surrounding air density, p, and viscosity, µ, and velocity, V. Using p, V, and W as repeating variables, express this relationship in dimensionless form.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.18P: The drag on an airplane wing in flight is known to be a function of the density of air (), the...

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An airplane builder wants to build a scaled-down model of a real airplane in a 12:1 ratio in order to be able to perform tests in a wind tunnel. The real plane flies at 126 km/h, while the air speed in the tunnel where the model is located is given by V. The performances of the two will be equivalent for a value of V, in m/s, equal to Data: air viscosity η = 1.8 × 10-5 kg/(m.s) air density ρ = 1.3 kg/m3
Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V, pressure difference DP, fluid density r and viscosity m. a)Determine dimensionless P groups. b)A test is to be performed for a large pump that delivers 1.5 m3 /s of water from 40 cm diameter impeller with pressure rise of 400 kPa. For the test, a model with an 8 cm diameter impeller is to be used. What flow rate should be used and what would be the pressure rise in model pump. Note: The model fluid is water at same temperature as the water in the prototype.
A dimensionless combination of variables that is important in the study of viscous flow through pipes is called the Reynolds number, Re, defined as ???/? where, as indicated in Fig. 11, ? is the fluid density, V the mean fluid velocity, D the pipe diameter, and the fluid viscosity. A Newtonian fluid having a viscosity of 0.38 ? . ?/?² and a specific gravity of 0.91 flows through a 25‐mmdiameter pipe with a velocity of 2.6 ?/?. Determine the value of the Reynolds number using (a) SI units, and (b) BG units.
The variables in a Saybolt viscometer are the time (t) required to empty a certain volume of oil of density (ρ) and viscosity (μ), a length (L) representing the dimensions of the viscometer, and the gravitational acceleration (g). Using the Buckingham Pi-theorem, show that
The force, F, acting on a billboard due to wind depends on it length, l, height, h, the modulus of elasticity of the board, E, and the specific weight, γa, of the air. Using dimensional analysis, find an appropriate dimensionless relationship.
At a sudden contraction in a pipe the diameter changes from D, to D2. The pressure drop, Ap, which develops across the con- traction is a function of D, and Dz, as well as the velocity, V, in the larger pipe, and the fluid density, p, and viscosity, u. Use D, V, and u as repeating variables to determine a suitable set of dimensionless parameters. Why would ti be incorrect to include the velocity in the smaller pipe a sa nadditional variable?
For most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases: a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.
Let the velocity, u (m/s), specific heat, cp (kJ/(kg K)), and temperature, T (K), be used to define a dimensionless number given by u2cpaTb. The powers must be a=[Blank-1] and b=[Blank-2].
When using the method of repeated variables in a problem, it is determined that one of the independent Πs is given by the product between the independent variable lift force FL [N], and the repeated variables density ρ [kg/m3], velocity V [m/s], and area A [m2]. Remembering that Πs are given by the product of the primary dimensions raised to the zero power, of the type m0L0t0 T0, determine this independent Π. (the form is in the side picture)
The water resistance (drag) R on the submarine Nautilus is a function of its length L, velocity v of the ship, viscosity μ, and density ρ of the water in which it moves. Determine dimensionless groups that could be used to organize test data.
In supersonic wind tunnel testing, if different gases areused, dynamic similarity requires that the model and prototypehave the same Mach number and the same( a ) Euler number, ( b ) speed of sound, ( c ) stagnation enthalpy,( d ) Froude number, ( e ) specific-heat ratio
Table 1 shows the variation of dynamic viscosities of water with absolute temperature. Table 1: Dynamic viscosity of water with absolute temperature. Viscosity µ, Pa.s x 10-³ 1.787 Temperature, K 273.15 278.15 283.15 293.15 303.15 1 313.15 333.15 353.15 373.15 4G 1.519 1.307 1.002 0.7975 0.6529 0.4665 0.3547 0.2828 a) Using excel software, develop a relationship of for viscosity in the form of μ=A+BT+CT² + DT³ + ET. Done Show your trend line regression and standard deviation for linear and polynomial index (quadratic T², cubic T³ and T). b) Using the relationship developed, predict the dynamic viscosity of water at 50 °C at which the reported value is 5.468 x 10 Pa.s. Compare your result with the results of Andrade's equation which is given in the form of μ = D.e BT where D and B are constants whose values are to be determined using viscosity data given.