PHYSICS SET UP

Ray Williams

April 13, 2013

TRIDENT UNIVERSITY Module 4 - Case Fluid Mechanics Ray Williams 4/23/2013

Module 4 - Case

Fluid Mechanics

1. A laboratory receives a sample of a metallic alloy composed of aluminum and magnesium. The sample is a solid cylinder with a diameter of 2 cm and a length of 5 cm. Its mass is 15.70 g. What is its density? What is its specific gravity?

d = 2cm, r = 1cm, h = 5 cm

M = 15.70 g

Volume of alloy = πr2h = 15.707 cm3

Density_alloy = mass / volume = 15.70g / 15.707 cm3 = 1 g / cm3 = 1000 kg/m3

Specific gravity = Density_alloy / Density (of magnesium) = 1000kg/m3 / 1738 kg/m3 = 0.5754

ANSWER1: 1000kg/m3

ANSWER2: 0.5754

2. A boat has a dry weight of 3500 lbs. How many liters of water does it displace?

SHOW WORK: 3500lbs=1587.5734Kg

displace water =weight of boat=1587.5734 Kg=1587.5734 *1.03 L =1635.2 liters

ANSWER: 1635.2 liters

3. A steel pipe runs vertically from the floor of the ocean to the surface. The pipe is empty -- that is, contains air at atmospheric pressure . What is the water pressure on the pipe 200 m below the surface? At that point, what is the force on 1 cm2 of the pipe wall? (Density of seawater = 1.03 kg/L)

SHOW WORK: P @200 m below=P0+density*g*h =1.01325*10^5 +(1030*9.81*200) =2122185 N/m2 =20.944 atm force on pipe wall=P*A =2122185*(10^-4) =212.22 N

ANSWER1: 20.944 atm

ANSWER2: 212.22 N

4. Water is flowing through a circular pipe with an internal diameter of 1 meter, at a rate of 0.5 m3/s. What is the water's flow velocity? What is its dynamic pressure?

SHOW WORK: water flow velocity=(0.5 m3/sec)/(pi/4)(1^2) v =0.6367 m/sec dynamic pressure=(1/2)*density*(v^2) =327.9 Kg/(m^2 sec)

ANSWER1: 0.6367 m/sec

ANSWER2: 327.9 Kg/(m^2 sec)

5. The static water pressure at point 1 in a pipe is 100 kPa, and the fluid velocity is 2 m/s. At point 2 downstream, the pipe widens and the velocity decreases to 1 m/s. What is the static pressure at that point? The usual assumptions concerning laminar flow, no friction losses, incompressibility, etc. all apply

SHOW WORK: P1+(1/2)*density*v1^2+density*gh=P2+(1/2)*density*v2^2+density*gh

* P1+(1/2)*density*v1^2=P2+(1/2)*density*v2^2

*100000+(1/2)*1030*(2^2)=P2+(1/2)*1030*(1^2)

* P2=101545 Pa

*P2=101.545 Pa

ANSWER: P2=101.545 Pa