10) The shape of a rain drop falling in the athmosphere is given by the following formula developed from photographic studies related to the fall event : o = (v-v.).d./H. Find the dimension of H by Dimensional Analysis. where, y : weight density of falling fluid drop, Vo: weight density of surrounding vapor, de: equatorial diameter of the falling fluid drop, H:a function found in the experiment (coefficient), a : surface tension.

10) The shape of a rain drop falling in the athmosphere is given by the following formula developed from photographic studies related to the fall event : o = (v-v.).d./H. Find the dimension of H by Dimensional Analysis. where, y : weight density of falling fluid drop, Vo: weight density of surrounding vapor, de: equatorial diameter of the falling fluid drop, H:a function found in the experiment (coefficient), a : surface tension.

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 5.13P: 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its...

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5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.
Question 3 The power, P, to drive an axial pump is in a function of density of fluid, p, volumetric flow rate, Q, pump head, h, diameter of rotor, D, and angular speed of rotor, N. (a) (b) (c) P PDS N3 Verify that - is a dimensionless group. Determine the remaining pi group and perform dimensional analysis. Define geometric similarity and dynamic similarity. Categorize the pi group obtained from part (b) as geometric similarity or dynamic similarity, respectively.
b) When a liquid in a beaker is stirred, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (o) of the whirlpool, fluid density (p), gravitational acceleration (g), and radius (R) of the container. Take o, p and R as the repeating variables.
The power P required for operating a pump depends on the diameter of the pump D, the pressure rise Ap across the pump, the fluid density p, the fluid viscosity and the Theorem, and D, Q and p as the repeating variables, the dimensionless group associated with μ is given by volume flow rate Q through the pump. Using Buckingham's μDªQbpº. Determine the values of a, b and c. 1. [0.99, 1.01 2. [-1.01, 0.99 3. [-1.01, -0.99 a= b = C=
Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k.
b) The following shear stress – shear rate behavior was observed. Shear rate (Seconds-1) Shear Stress (dynes/cm?) 20 11 30 15.2 40 19.1 50 22.9 60 26.5 1. Make a plot of shear stress (ordinate) vs shear rate (abscissa) on log-log paper. 2. Can the fluid behavior be accurately modeled by the Newtonian, Bingham plastic, or Power law model?
c) When small aerosol particles move through air or water, the Reynolds number is very small (Re < 1). Such flows are called creeping flow. The aerodynamic drag on an object in creeping flow is a function only of its speed, V some characteristic length scale, L of the object and fluid viscosity, µas indicated in Figure 11. Use dimensional analysis to generate a relationship for Fp as a function of the independent variables. The dimensions of Fp are MLT2. FD L Figure 11
When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.
1- The pressure drop, Ap, along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, {, between pressure taps. Assume that Ap is a function of D and €, the velocity, V, and the fluid viscosity, u. Use dimensional analysis to deduce how the pressure drop varies with pipe diameter. A Qulindor with a diametor D doota unr ht in g liquid Whon tha
The conduction heat transfer in an extended surface, known as a fin, yields the following equation for the temperature T, if the temperature distribution is assumed to be one-dimensional in x, where x is the distance from the base of the fin, as shown in figure: To Fin >X T(x) h,T Heat Loss d²T_hp (T-T) = 0 dx² ΚΑ dT dx = 0 Here, p is the perimeter of the fin, being 2R for a cylindrical fin of radius R; A is the cross-sectional area, being R2 for a cylindrical fin; k is the At x = 0: T = T₁ dT At x=L: :0 dx thermal conductivity of the material; T is the ambient fluid temperature; and h in the convective heat transfer coefficient. The boundary conditions are as follows: where L is the length of the fin. Solve this equation to obtain 7(x) by using Euler's method for R=1cm, h= 20 W/m².K, k = 15 W/m-K, L = 25 cm, T₁ = 80°C, and T = 20°C.
A dimensional analysis is performed on the drag on a boat. When the effects of viscosity can be neglected, the Euler number based on the drag D experienced by the boat is a function of a Froude number. The effects of the dimensions of the boat can be represented by its length I. The drag on a model of the model is measured as 0.35N. If the ratio of / for a full-scale model to the value of/ for the model is 46, calculate the expected drag on the full-scale boat. Your answer should be to the nearest kN. The properties of the water in the model test matches those for the full-scale boat.