Análisis Dimensional PDF

# TRABAJO RETO DE ANÁLISIS DIMENSIONAL 1. The variation of the pressure per unit of length depends on the weight of the water through the pipe, the speed of the water and the acceleration of gravity. Determine the most appropriate formula that represents this truth, being k a constant. 2. If the...

# TRABAJO RETO DE ANÁLISIS DIMENSIONAL 1. The variation of the pressure per unit of length depends on the weight of the water through the pipe, the speed of the water and the acceleration of gravity. Determine the most appropriate formula that represents this truth, being k a constant. 2. If the following expression is dimensionally homogeneous, determine the dimensions of "Q": $Sen\theta = \frac{PRx + QBz}{m}$ Where: - m = mass - R = radius - x = time - B = force - Z = velocity 3. The equation of a physical phenomenon is: $V = \frac{3V^2*a*Fy}{Sen(zay)} - xF$ Where V = velocity, F = force, a = acceleration. The dimensions of z are: 4. What should be the value of P so that the expression is dimensionally correct? $\sum_{i=1}^{n}D_1*c*e= \frac{e^{-Pvt}}{D_0}$ Where v = linear velocity; D0, D1 = Density; c,e = length and $[t]=ML^{-1}T^{-1}$, the dependence of "vc" with η, ρ, D and R is: 5. Find the dimensional equation of K, if: $K^2 = \frac{F}{6\sqrt{PD^2V^{-1}}}$ Where: F = Force; P = Pressure; D = Density v = Velocity. 6. The density of the magnetic flux B, originated by a rectilinear current I, at a radial distance r, is given by the following relation: $B = \frac{\mu I}{2\pi r}$ Find the unit (in the S.I) of the magnetic permeability μ. (1 Henry (H) = 1 m².kg. s-2. A-2) 7. Find the dimensional equation of X in the following equation: $\frac{F}{V} = \frac{9,8 * P * \sqrt{5} * m * sen(37°) }{X}$ Where P is power, V is volume, 9.8 is the acceleration of gravity, F is force and m = length. 8. The critical velocity "v" at which the flow of a liquid through a pipe becomes turbulent, depends on the viscosity "η", the density "p" of the fluid, the diameter "D" of the pipe and a dimensionless constant "R". If $[n] = MLT^{-1}$, the dependence of "v" with η, p, D and R is: 9. A system of units is created where velocity, mass and force are considered as fundamental magnitudes. Find the dimensional equation of "E" in this new system, if E = pressure x density. In this new system it is defined: [velocity] = A; [mass] = B and [force] = C. 10. The electric potential energy (UE) is expressed for a specific case as: $U_E = \frac {kQ^2}{d}$ Where: Q = electric charge, d = distance. Find [K].