Teste_4_SEM0403_2osem_2020 (1)

Prévia do material em texto

Universidade de São Paulo
Escola de Engenharia de São Carlos
Teste 4: SEM 0403 - Fundamentos da Mecânica dos Fluidos (II sem. 2020)
Data de entrega: 16 de outubro de 2020
Por favor, resolver o teste de forma clara e detalhada. Enviar arquivo em formato .pdf
na melhor resolução possível. O nome do arquivo deve conter o número do grupo e do
teste, e.g., Grupo_1_Teste_4.pdf
1. Figure simulates a manifold flow, with fluid removed from a porous wall or perforated section of
pipe. Assume incompressible flow with negligible wall friction and small suction Vw ≪ V1. If (p1, V1,
Vw, ρ, D) are known, derive expressions for (a) V2 and (b) p2.
Figure: Exercise 1
2. A sharp-edged splitter plate inserted part way into a flat stream of flowing water produces the flow
pattern shown. Analyze the situation to evaluate θ as a function of α, where 0 ≤ α < 0.5. Evaluate
the force needed to hold the splitter plate in place. For what value of α is the force maximum?
Figure: Exercise 2
Oscar
Realce
Oscar
Texto digitado
Oscar
Caixa de texto
22
2
3. Analyze the design of a cart propelled along a horizontal track by a water jet that issues under
gravity from an open cylindrical tank carried on board the cart. (A water-jet-propelled cart is shown
in the Figure) Neglect any change in slope of the liquid free surface in the tank during acceleration.
Analyze the motion of the cart along a horizontal track, assuming it starts from rest and begins to
accelerate when water starts to flow from the jet. Derive algebraic equations for the acceleration and
speed of the cart as functions of time.
Figure: Exercise 3
4. A flat plate is hinged at one side to the floor, as shown, and held at a small angle θ0 (θ0 ≪ 1)
relative to the floor. The entire system is submerged in a liquid of density ρ. At t = 0, a vertical force
is applied and adjusted continually so that it produces a constant rate of decrease of the plate angle
θ.
−dθ
dt
= ω = Const,
Find the horizontal force F (t) exerted by the hinge on the floor (assume the plate has negligible mass).
Figure: Exercise 4
3
5. Water flows vertically upward in a circular cross-sectional pipe as shown in Figure. At section (1),
the velocity profile over the cross-sectional area is uniform. At section (2), the velocity profile is:
V = wc
(
R− r
R
)1/7
k̂
where V = local velocity vector, wc = centerline velocity in the axial direction, R = pipe radius, and
r = radius from pipe axis. Develop an expression for the fluid pressure drop that occurs between
sections (1) and (2). Consider the weight of the water column and the pipe wall friction. Explain
physically the result. What happens if the velocity profiles are identically parabolic at sections (1) and
(2)? What happens if the pipe is horizontal? What happens if the water flows vertically downward?
Justify mathematically.
Figure: Exercise 5