A solid cylindrical needle of diameter d, length L, and density p may float in liquid of surface tension I. Neglect buoyancy, assume a contact angle of 0 degrees and that the needle is submerged upto the diameter line. (1) Draw the free body diagram indicating the force due to surface tension and the weight of the needle. Given that d << L for a typical needle, can you simplify the surface tension forces? (2) Using the simplification, derive a formula for the maximum diameter dmax such that the cylinder is able to float in the liquid.

A solid cylindrical needle of diameter d, length L, and density p may float in liquid of surface tension I. Neglect buoyancy, assume a contact angle of 0 degrees and that the needle is submerged upto the diameter line. (1) Draw the free body diagram indicating the force due to surface tension and the weight of the needle. Given that d << L for a typical needle, can you simplify the surface tension forces? (2) Using the simplification, derive a formula for the maximum diameter dmax such that the cylinder is able to float in the liquid.

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

The U-tube in Fig. is open at A and closed at D. Ifaccelerated to the right at uniform a x , what acceleration will cause the pressure at point C to be atmospheric? Thefl uid is water (SG = 1.0).
What will be the diameter (in mm) of a water droplet, the pressure inside which is 0.00221 N/cm2 greater than the outside pressure? (Take surface tension as 0.075 N/m)
FLUID MECHANICS : HYDROSTATICS Answer: 218kN, 180kN, 191kN
In Fig. , a one-quadrant spherical shell of radius R issubmerged in liquid of specifi c weight γ and depth h >R.Find an analytic expression for the resultant hydrostaticforce, and its line of action, on the shell surface.
A plastic spherical balloon is held below the surface of a swimming pool by a cable tied to a bottom of the pool . The spere has a volume of 1.5×10^-2 m^3 and the tension in the cable is 90 N. a. What is the buoyant force exerted by the water on the sphere b. Calculate the mass of the balloon c.
I am working on practice problems and am stuck on this question.
3. Consider a hot-air balloon with fixed volume VB = 1.1 m³. The mass of the balloon envelope, whose volume is to be neglected in comparison to VB, is m̟ = 0.187 kg. The balloon shall be started, where the external air temperature is T1 = 20°C and the normal %3D
Air P Question 5. 1,2 m wide AB gate is articulated from point A shown in the figure. The heights of the fluids are 6 and 2 for h1 and h2, respectively. Water A hi Considering the measured pressure P = -15 kN/m?, find the magnitude of the force Oil h2 *(kN) that will affect point B, in which the в force provides the balance in AB gate (SGoil = 0,75). Figure 5
A conical vessel r=(b-z)tanA, rests with its open end downward on a flat surface, as shown in the figure. We want to fill it to a height h with a liquid of density p. What will be the lifting force on the vessel? (tanA: tangent of A)
Problem 3 A gate is 1.5m in width and hinged at point A. Another point on the gate, B, is resting against a smooth wall. What is the total hydrostatic force (due to the seawater, SG=1.03)? What are the reactions on points A and B, neglecting the weight of the gate? [21 8kN, 180KN, 191KN) Seawater Wall SG-1.03 gate 2m 3m Hinge
Problem 3.- Blaise Pascal doubled Torricelli's barometer using Red wine, with a density of 984kg / m3 . (a) What was the height h of the wine column for normal atmospheric pressure? (b) Would you expect the emptiness on the column ti be as good as for mercury? Explain and argue.
Water flows through a constricted pipe at a uniform rate. At one point, the diameter of the pipe is 0.056 m and the pressure is 5.7 x 104N/m2. At another point, 0.8 m higher than the previous point, the diameter is 0.023 m and the pressure is 1 X 104N/m2 . Calculate the velocities at the lower section and the upper section. Also calculate the rate of flow. Density of water = 1000 kg/m3.