Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?

Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

C1 (a). A lubricating oil having the dynamic viscosity of 0.056 poise and specific gravity of 1.17. Calculate (i) the density of oil in kg/m3, (ii) the weight density of oil in N/m3, (iii) the kinematic viscosity in stokes, and (iv) the specific volume in m3/kg. C1 (b). The capillary effect in a glass tube of 2.8 mm diameter, when immersed in (1) water and (2) mercury are 7.7 mm and -3.5 mm respectively. Calculate the value of surface tension in contact with air for water and mercury in N/m. Take, the contact angle for water =0° and mercury =130°. C1(a). (i).the density of oil in kg/m3 C1(a). (ii) the weight density of oil in N/m3 C1(a). (iii) the kinematic viscosity in stokes C1(a). (iv) the specific volume in m3/kg C1 (b). 1.the value of surface tension (water) in N/m C1 (b). 2. the value of surface tension (mercury) in N/m
Figure shows the flow of water over a dam. Thevolume fl ow Q is known to depend only on crest width B ,acceleration of gravity g , and upstream water height Habove the dam crest. It is further known that Q is proportionalto B . What is the form of the only possible dimensionallyhomogeneous relation for this flow rate?
Problem 1: The discharge pressure (P) of a centrifugal pump shown below is a function of flow rate (Q), impeller diameter (D), fluid density (p), and impeller angular speed (12). P = f (Q. D, p. 92). Use the Buckingham pi technique to rewrite this function in terms of dimensionless parameters, 1 g (n₂). P= P(Q,D, Dimensions 2) N= 5 Q. P
Suppose we know little about the strength of materials butare told that the bending stress σ in a beam is proportionalto the beam half-thickness y and also depends on thebending moment M and the beam area moment of inertiaI . We also learn that, for the particular case M = 2900in ∙ lbf, y = 1.5 in, and I = 0.4 in4 , the predicted stressis 75 MPa. Using this information and dimensional reasoningonly, find, to three significant figures, the onlypossible dimensionally homogeneous formula σ=y f ( M , I ).
A- 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 species
During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .
Consider a boundary layer growing along a thin flat plate. The boundary layer thickness & at a downstream distance x is a function of x, the fluid density p, dynamic viscosity, and free stream velocity V. Use Buckingham's theorem with p, x and V as repeating variables, to obtain the relationship between dimensionless parameters Is. Figure 3.2
Show that Reynold number, pud/µ, is non-dimensional. If the discharge Q through an orifice is a function of the diameter d, the pressure difference p, the density p, and the viscosity µ 1/2 1/2 show that Q = C p?d²/p2 where C is some function of the nondimensional group (dp"“p"
An important parameter in fluid flow problems involving thin films is the Weber number (We) which can be expressed in equation form as We=[pv^2L/(omega)] where p is the density of the fluid, v is a velocity, L is a length, and (omega) is the surface tension of the fluid. If the Weber number is dimensionless, what are the dimensions of the surface tension (omega)?
An incompressible fluid oscillates harmonically (V = Vosinut, where Vis the velocity) with a frequency of 9 rad/s in a 6-in.-diameter pipe. A 1/5 scale model is to be used to determine the pressure difference per unit length, Ap, (at any instant) along the pipe. Assume that Api= f(D, Vo, w, t, u, p) where D is the pipe diameter, w the frequency, t the time, the u fluid viscosity, and p the fluid density. If the same fluid is used in the model and the prototype, at what frequency should the model operate? Wm i rad/s
Velocity distribution of a fluid in a sliding plate viscometer is used to measure the viscosity of the fluid. The top plate is moving with force (F) with a constant velocity (V) as shown in the Figure below. Force (Ft)= 5 N, Velocity (V) = 10 m/s, Temperature = 100°F. Top plate (Area » Length = 0.1 m and width = 0.05 m spaced by 0.001 m) is moving and the bottom plate is stationary. Determine: The viscosity of the fluid. Which fluid is this? Is this fluid more, or less viscous than water? ● IN FLOW N-L
Problem 4: The power P developed by a wind turbine is a function of diameter D, air density p, wind speed V, and rotational rate @. Viscous effect is negligible. (4a) Rewrite the above relationship in a dimensionless form; (4b) In a wind tunnel, a small model with a diameter of 90cm, rotating at 1200 RPM (revolution per minute), delivered 200 watts when the wind speed is 12m/s. The data are to be used for a prototype of diameter of 50m and wind speed of 8 m/s. For dynamic similarity, what will be (i) the rotational speed of the prototype turbine? (ii) the power delivered by the prototype turbine? Assume air has sea-level density.