Mechanical Engineering: Fundamentals of Fluid Flow exam

(Fall 2018) ME721 Fundamentals of Fluid Flow

Homework Assignment #2 (Due date: 10/25/2018)

(*) Please include all the intermediate steps.

1. (20 points) Water flows at a uniform speed out of a round pipe vertically downward onto a

horizontal flat plate a distance 𝐿 = 10 cm below. The volumetric flow rate is 𝑄 = 100 cm3/s, and the

pipe area is 𝐴 = 1.0 cm2. The water spreads out smoothly over the plate so that at a distance r from

the flow axis the radial velocity 𝑉𝑟(𝑟) is uniform, i.e., independent of 𝑧. The flow is axisymmetric so

that the thickness of the water layer ℎ(𝑟) depends only upon 𝑟. We assume that the flow is inviscid

and that the streamline is well defined. Derive expressions for 𝑉𝑟(𝑟) and ℎ(𝑟), assuming that ℎ ≪ 𝐿, and calculate their values at 𝑟 = 10 cm.

2. (20 points) A conical funnel of height H and semi-vertex angle  has a small outlet hole of area A «

H2. At t = 0 the funnel is filled with water, which is then allowed to drain out through the hole. We

assume that the flow is inviscid and that the streamline is well defined. We also assume that, at any

time, the flow is quasi-steady, so we can apply the Bernoulli equation to calculate the flow velocity

𝑣(𝑡) at the funnel. Derive an expression for the time t required for the funnel to become empty.