Bill is working on an electrical circuit problem. He remembers from his electrical engineering class that voltage drop
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Fluid Mechanics: Fundamentals and Applications
- Some children are playing with soap bubbles, and you become curious as to the relationship between soap bubble radius and the pressure inside the soap bubble . You reason that the pressure inside the soap bubble must be greater than atmospheric pressure, and that the shell of the soap bubble is under tension, much like the skin of a balloon. You also know that the property surface tension must be important in this problem. Not knowing any other physics, you decide to approach the problem using dimensional analysis. Establish a relationship between pressure difference ΔP = Pinside − Poutside, soap bubble radius R, and the surface tension ?s of the soap film.arrow_forwardThermal 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.arrow_forwardStorage is required for 35000 kg of propane, received as a gas at 10 °C and 1 atm. Your engineering team was tasked to propose a suitable method of storage. One of the proposed methods is to store the gas in a cylinder tank as gas at 10 °C and 1 atm. You need to calculate the volume of the tank required to support your proposal. You decided to use the truncated Virial Equation to find the volume required. Discuss whether the proposed storage can be implemented in terms of the dimension of the tank and cost.arrow_forward
- Check the following equation for dimensional homogeneity: mu = (Fcos) at where m is mass, v is velocity, F is force, is an angle, and it is time. Check that each term in the equation has the following dimensions: [MOLT] where you are to choose the coefficients a, b, c. Answers: b= C= i iarrow_forwardWater X 50-mm inside diameter The volume flow rate of the system The pressure at the point "A" The pressure at the point "B" 25-mm diameter As a consultant at one of the country's leading soft drink companies, you are tasked with evaluating the system depicted to determine the following parameters using Bernoulli's Equation if the values assigned to "X" and "Y" are 3m and 0.5m respectively: i. ii. iii.arrow_forward. I am planning to perform some volume-flow rate measurements in the Fluid Mechanics Laboratory. For this, I need a volumetric measuring tank (graduated cylinder) and a stopwatch. I considered the volume of the measured tank as 15 gallons and a stopwatch with reaction time as 1/10th of a second (though resolution of 1/1000th of a second). What is the volume flow rate if it takes 5 minutes to fill a 15-gallon of tank? Determine the smallest division to be on the tank in order to estimate the volume flow rate within an accuracy of ± 0.05 gpm.arrow_forward
- Write the primary dimensions of each of the following variables from the field of solid mechanics, showing all your work: (a) moment of inertia I; (b) modulus of elasticity E, also called Young’s modulus; (c) strain ? ; (d) stress ?. (e) Finally, show that the relationship between stress and strain (Hooke’s law) is a dimensionally homogeneous equation.arrow_forwardThree students at NUST derive the following equations in which x refers to distance traveled, v the speed, a the acceleration (m/s2), and t the time, and the subscript (0) means a quantity at time t=0: (i) x=vt2+2at, (ii) x= v0t +at2 (iii) x=v0t +2at2 Which of these could be possibly be correct according to a dimensional check?arrow_forwarda)Weber number (We) represents the ratio of disruptive hydrodynamics forces to the stabilizing surface tension force. It is an important dimensionless parameter applied during the analysis of thin film flows, which examines the ratio between inertia force and surface tension force acting on a fluid element. Using The Buckingham Pi Theorem, generate the formula for We. We is a function of fluid density (ρ), fluid velocity (v), characteristic length (l) and surface tension (σs), which can be mathematically written as: ?? = ?(?,?,?,??) b)Froude number (Fr) is an important dimensionless parameter used in open channel flow. Give the physical and mathematical definition of Fr. Prove that Fr is dimensionless.arrow_forward
- You are tasked with designing the runway on an aircraft carrier. The minimum speed for the F/A-18 Hornet is 193.8 mph. The Hornet weighs 40,000 lbf and its twin engines provide a thrust of ~40,000 lbf combined, providing a max acceleration of 1g. How long must the deck be to takeoff unassisted in feet?arrow_forwardThe 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.arrow_forwardCheck the following equation for dimensional homogeneity: mv = = 1.5² (Fcose) dt where m is mass, v is velocity, F is force, is an angle, and t is time. Check that each term in the equation has the following dimensions: [MªLbTC] where you are to choose the coefficients a, b, c. Answers: a = i b = i C=arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning