ME 309 – Fluid Mechanics

Spring 2016

ME 309 – Fluid Mechanics

Spring 2016

ME 309 – Fluid Mechanics

Spring 2016

ME 309 – Fluid Mechanics

Spring 2016

ME 309 – Fluid Mechanics

Spring 2016

ME 309 – Fluid Mechanics

Spring 2016

A vertical jet of water is created from a water tank with a constant water level which is10 meters above

the ground (enforced by adding the water into the tank). The water jet impinges on a 2 kg horizontal

brick. When the brick is 5 meter above the ground, the brick is moving downward at V= 2 m/s. The area

of the nozzle exit Ao is 0.0001 m 2 . Ignore the friction on the water, using g = 10 m/s2

a) compute the jet velocity Vo at the nozzle exit.

b) compute the vertical acceleration of the disk at this instant.

c) compute the vertical force exerted on the brick by the water jet at this instant.

Solution:

a)

Applying Bernoulli’s equation between free surface and nozzle exit.

+ = +

= 2 = √200 = 14.14

/ b)

Drawing CV. (On control surface everywhere atmospheric pressure)

Assumption:

1. Steady flow1 in C.V

2. Uniform flow on the control surface.

3. Mass of water in C.V. is negligible

Applying Bernoulli’s equation between free surface and the lower surface of CV.

+ = + ( − ℎ)

= 2 ( − ℎ) = 10 /

Using COM:

∙ " = ∙ "

"

COLM:

#$%%&’%&() 345 ,-.0 +.%%&345 ,

.%%&345 ∙-6%%%%%&

/7

On Y axis:

8 9 :

: "

: ; 12

/

9 : : " 10

0.1808 /

8

c)

89 >?@A 8 B

?@A

4. Problem 3 - [25 points total] A tank (size WT = 0.5 m; LT = 1 m) is filled with water up to the level H = 0.5 m. A block of wood is

pivoted along one edge as indicated in figure. The block shape and size is detailed in the figure

below. The block is in equilibrium when immersed in water to a depth of h = 0.06 m.

a. (8 points) Determine the magnitude and the point of application of the horizontal force acting

on the left surface of the block.

b. (12 points) Determine the density of the wood material.

c. (5 points) Determine if the block is still in equilibrium with the same h in case of a wider

tank (WT = 1 m)

Assume g = 9.81 m/s2 as value for gravity and ρwater = 1000 kg/m3.

ME 309 – Fluid Mechanics LAST NAME: ___________________________

Spring 2016 FIRST NAME: ___________________________