Assume that the tip deflection ô of a cantilever beam is a function of the tip load P, beam length L, area moment of inertia I, and material modulus of elasticity E; that is, & = f(P, L, I, E). Rewrite this function in dimensionless form, and comment on its complexity and the peculiar value of j.

a string is attached to a mechanical vibrator, which has a frequency of 30Hx. the sttring is 3.0m long and has a linear density of .4 g/cm. the tension is varied by adding weights to teh string passing over the pully. What tension is needed to cause the string to resonate with the vibrator in four segments. assume that he points where the string meets the vibrator and the pulley are approx nodes.

Q4: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr = and the Reynolds number (Re pch. are relevant dimensionless parameters Fr = f (Re). The wave speed c of %3D waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity u. P. u Figure 1

Ів 00 WB WC DBC A LA WA P lc UBC Engineering A kid excitedly swings his foam cut-out hammer. If point P acts like a pin and the hammer rotates about kg that point, what is the moment of inertia of the hammer? The foam has a density of p = 150 and a uniform thickness of t = 0.5 cm. Assume each cut-out is a rectangular plate and the foam acts as a rigid body. m³ Plate A has a length 14 = 34 cm and width w₁ = 8 cm. Plate B has a length 13 = 8.5 cm and width wB = 30 cm. Plate C is identical to plate D, and has a length lc = 15 cm and width wc = 5 cm. Plate C and D are attached to plate B such that their centers line up. Ip = 0.00758 x (kg) - m²

fluid mechanics 1

Section 1.5 Problem 1. Mark each statement True or False, and justify your answer. (T/F) A homogeneous equation is always consistent. (T/F) If x is a nontrivial solution of Ax=0, then every entry in x is nonzero. (T/F) The equation Ax=0 gives an explicit description of its solution set. (T/F) The equation x = xu+xiv, with xa and xx free (and neither u nor va multiple of the other), describes a plane through the origin. (T/F) The homogeneous equation Ax=0 has the trivial solution if and only if the equation has at least one free variable. (T/F) The equation Ax=b is homogeneous if the zero vector is a solution. (T/F) The equation x = p + tv describes a line through v parallel to p. (T/F) The effect of adding p to a vector is to move the vector in a direction parallel to p.

(k - 1)/k P2 Tds relationship: Tds = dh -vdp. Start from the Tds function, please derive that . Please T1 P1 list clearly the assumptions/conditions applied for the derivation

Two dimensional stress tensor at a point is given by a matrix Ox To 100 30 5x 0 30 20 The maximum shear stress is MPa MPa.

Please see attached photo for question information. Thanks

As shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid density p, width of the cylinder d, freestream velocity V, and fluid viscosity u. (a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the primary dimensional. Use p, V, and d as the repeating parameters. (b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2. Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding frequencies. -Vortices V