• If (see attachment) find the acceleration field of this flow. Is this a steady flow? • If the velocity field of a flow is given by (see attachment) where (see attachment) and Q is a positive constant. Find the acceleration field.
Gradients : Proof of Identites
Show that grad x (FxG)=....
Archimedes' Principle, Euler's Equations, Buoyancy and Hydrostatic Pressure
Recall the standard vector identity: {see attachment} • A body is immersed in water at rest, under gravity. Show from Euler's equations that the pressure is: {see attachment} (Hydrostatic pressure) • Deduce that the buoyancy force on the body is equal to the weight of water displaced by it. • A boat floats on a pond. ...continues
Inviscid Fluid and Velocity Field : Pressure, Density and Gravitational Acceleration
Consider a inviscid fluid with velocity field {see attachment} Find the pressure of the fluid as a function of the density and the gravitational acceleration in each case.
Solution Concentrations : Percentages and Amount of Concentrate Needed
I am doing an embalming course and need to work out percentages , e.g of question. A container will hold 1 ltr, you will need the following solutions for different purposes, how much concentrate will you need in each case. 2% solution 1 in 20 solution 4 in 50 solution a 5.5 solution 1 in 3.5 solution. Can you show m ...continues
Sound Wave Equation : Proof of Solution
Consider the wave equation in one space dimension: ..... show that the function ..... where f,g are arbitrary twice differentiable functions, is a solution to the wave equation.
Wave Equation : D’Alembert’s Solution
Given that the general solution to the wave equation in one space dimension is given by where f, g are arbitrary twice continuously differentiable functions deduce that the solution s satisfying the initial conditions and for some function v, is (this is a special case of the so called D’Alembert’s solution of ...continues
Consider the wave equation when the solution s admits spherical symmetry, ie, s(t,x,y,z)=v(t,r), where ... , the wave equation becomes: (1) making the substitution for some twice differentiable function h, show that (1) becomes hence, show that the general solution reads for any twice differentiable functions f ...continues
Hazen-Williams Formula : Find the Diameter of a Pipe
The length of cast-iron pipe is to be 4200 ft., and the head causing flow is to be 12.6ft. After the pipe has been in service 5 years, it is expected to discharge water at a rate equal to 3.2 cfs. Using a Hazen-Williams Formula Chart in which C = 160 What is the diameter of the pipe? 16 in., 12 in., 14 in., 10 in. The head fl ...continues
Static Moment : Symmetrical Trapezoidal Plate in a Liquid
A symmetrical trapezoidal plate has the following dimensions: The width of the parallel sides are, respectively, 2.5 and 4.5 ft. The perpendicular distance between those sides is 1.5 ft. The plate is submerged in a liquid in a vertical position with the parallel sides horizontal and the shorter parallel side at the tip and exact ...continues
