5. The drag force, fd, on a sphere located in a pipe through which a fluid is flowing is to be determinedexperimentally. Assume that the drag is a function of the sphere diameter, d, the pipe diameter, D, thefluid velocity, V, and the fluid density, p. (a) What dimensionless parameters would you use for this prob-lem? (b) Some experiments using water indicate that for d = 0.2in., D = 0.5in, and V = 2ft/s, the dragis 1.5 x 10-3lb. Estimate the drag on a sphere located in a 2 - ft-diameter pipe through which water isflowing with a velocity of 6ft/s. The sphere diameter is such that geometric similarity is maintained. (Ans:31.11b)Sphere

The objective of the question is to determine the drag force on a sphere located in a pipe through…

Answered: 5. The drag force, fd, on a sphere…

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

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Ex. The force required to tow a 1:30scale model of a motor boat in a lake at a speed of 2m/s is 0.5 N, Assuming that the viscosity resistance due to water and air is negligible in comparison with the wave resistance, calculate the corresponding speed of the prototype for dynamically similar conditions. What would be the force required to propel the prptype at that velocity in the same lake? Ans.: 10.95m/s, 13500N
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 ).
Problem 5 s): The discharge pressure (P) of a screw pump (Fig. 5) is a function of flow rate (Q), screw diameter (D), fluid viscosity (u) and screw angular speed (w). P = f (Q, D, μ, w). Use the pi theorem to rewrite this function in terms of dimensionless parameters, ₁ g (T₂). Choose Q, D, and u as repeating variables. Screw Fig. 5: Screw pump
An underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60 m/sec with the following information, Poir at Standard atmospheric pressure = 1.18kg/m³ Pwater = 998kg/m3 Hair = 1.80 x 10-5 Pa-s at local atmospheric pressure and Hwater = 1 × 10-3 Pa-s then the pressure of the air in the model used times local atmospheric pressure is
The drag force (Fdrag) exerted by air on a moving car depends on a dimensionless drag coefficient (Carag), the specific volume of air (Vair), the velocity of the car (Var), and the frontal area of the car (Afront). (a) Based on unit considerations alone, obtain an equation for the drag force. Be sure to explicitly demonstrate that the final units are correct. (b) Explain, based on your equation, what happens to the drag force when each variable is changed in isolation. Indicate whether this predicted behaviour matches your intuition in each case.
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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 .
A uniform stream overflows in a circular cylinder and then a periodic Kármán vortex street is created. Through repeating variables, how can I create a dimensionless relationship for Kármán vortex shedding frequency (fk), where free-stream speed is V, fluid density is p, fluid viscosity is μ, and cylinder's diameter is d?
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
A football, meant to be thrown at 60 mi/h in sea-level air( ρ = 1.22 kg/m 3 , μ = 1.78 E-5 N . m 2 ), is to be testedusing a one-quarter scale model in a water tunnel ( ρ =998 kg/m 3 , μ = 0.0010 N . s/m 2 ). For dynamic similarity,what is the ratio of prototype force to model force?( a ) 3.86 : 1, ( b ) 16 : 1, ( c ) 32 : 1, ( d ) 56 : 1, ( e ) 64 : 1
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