Brad Peterson, P.E.Brad Peterson, P.E.

FRIDAYS – 14:00 to 15:40

FRIDAYS – 16:10 to 17:50

Class Website: https://sites.google.com/site/njut2009fall/

M P ’ E il Add Mr. Peterson’s Email Address: bradpeterson@engineer.com

Lesson 1, Properties of Fluids, 2009 Sept 04 ; 2009 Sept 18 Lesson 2, Fluid Statics, 2009 Sept 11; 2009 Sept 18 Lesson 2, Fluid Statics, 2009 Sept 11; 2009 Sept 18 Lesson 3, Hydrostatic Force on Surfaces, 2009 Sept 25 Lesson 4, Buoyancy and Flotation Lesson 5, Translation and Rotation of Liquid Masses

L 6 Di i l A l i d H d li Si ili d Lesson 6, Dimensional Analysis and Hydraulic Similitude Lesson 7, Fundamentals of Fluid Flow Lesson 8, Flow in Closed Conduits Lesson 9 Complex Pipeline Systems Lesson 9, Complex Pipeline Systems Lesson 10, Flow in Open Channels Lesson 11, Flow of Compressible Fluids Lesson 12, Measurement of Flow of Fluids

l d b l d Lesson 13, Forces Developed by Moving Fluids Lesson 14, Fluid Machinery

4.1. Archimedes’ Principle4.2. Measuring volume and specific gravity

using Archimedes’ Principle

The basic principle of buoyancy and flotation Discovered by Archimedes in about 200 B.C. Stated as follows:

b d fl b d fl d b d◦ A body floating or submerged in a fluid is buoyed (lifted) up by a force equal to the weight of the fluid displaced by the object.

Greek Engineer, I Ph i iInventor, Physicist, Mathematician

Archimedes Thoughtful by Fetti (1620)

The basic principle of buoyancy and flotation Discovered by Archimedes in about 200 B.C. Stated as follows:

b d fl b d fl d b d◦ A body floating or submerged in a fluid is buoyed (lifted) up by a force equal to the weight of the fluid displaced by the object.

A body floating or submerged in a fluid is buoyed (lift d) b f l t th i ht f th fl id(lifted) up by a force equal to the weight of the fluid displaced by the object.

Volumes of irregular solids can be calculated by measuring the loss of weight when an object is fully submerged

A stone weighs 90N in air. When immersed in water it weighs 50N. Compute the volume of the stone and its specific gravity.

50T N0

0B

YW T F

50T N

Water0B

B

W T FF W T 90W N

90 5090 50 40

B

B

F N NF N N N

BF

buoyant force 40BF N

340 9.8 kNN vm

33

40 0.0041 4.1 9800 /

Nv m litersN m

9800 /N m

weight of the stoneweight of the stonespecific gravity = weight of an equal volume of water

90specific gravity = 2 25Nspecific gravity 2.25

40N

An object that is 0.2m wide by 0.2m thick by 0.4m wide is found to weigh 50N in water at a depth of 0.6m. What is its weight in air and what is its specific gravitywhat is its specific gravity.

50 T N

0Y 0B

B

W T FW T F

W50 BW N F

BFBF

buoyant force weight of displaced liquid9 8

BFkN

3

9.8 (0.2 0.2 0.4 ) 0.157 157BkNF m m m kN N

m

50 50 157 207BW N F N N N

weight of the stonespecific gravity = i ht f l l f tweight of an equal volume of water

207specific gravity = 2.31157

NN

157N

A hydrometer is an instrument used toinstrument used to measure the specific gravity of liquids.

Remember, specific gravity is the ratio ofgravity is the ratio of the density of the liquid to the density of water.

A hydrometer weighs 0.0216N and has a stem at the upper end that is cylindrical and 2.8mm in diameter. How much deeper will it float in oil with sp gr 0 780 than in alchoholfloat in oil with sp gr 0.780 than in alchohol of sp gr 0.821?

hh

alcohol oilsp gr 0.821 sp gr 0.780

1For position 1 in alcohol compute v1For position 1, in alcohol, compute weight of hydrometer = weight of displaced liquid

v

13

9.80.0216 0.821 kNN vm

3 31

0.0216 0.000002680 821 9800 /

Nv m mN

6 31

0.821 9800 /2.68 10

Nv m

For position 2, in oilweight of hydrometer = weight of displaced liquid

9 8kN13

9.80.0216 0.780 ( )kNN v Ahm

3 31

0.0216( ) 0.000002830.780 9800 /

Nv Ah m mN

6 31( ) 2.83 10 v Ah m

6 31( ) 2.83 10 v Ah m

6 3 6 3

( )2.83 10 2.69 10 m mh

A

2 6 2(0.0028 ) 6.16 10 4

A

A m m

6 3 6 3

6 2

42.83 10 2.69 10 0.22 22

6 16 10m mh m mm

6 26.16 10 m

Lesson 1, Properties of Fluids, 2009 Sept 04 ; 2009 Sept 18 Lesson 2, Fluid Statics, 2009 Sept 11; 2009 Sept 18 Lesson 2, Fluid Statics, 2009 Sept 11; 2009 Sept 18 Lesson 3, Hydrostatic Force on Surfaces, 2009 Sept 25 Lesson 4, Buoyancy and Flotation Lesson 5, Translation and Rotation of Liquid Masses

L 6 Di i l A l i d H d li Si ili d Lesson 6, Dimensional Analysis and Hydraulic Similitude Lesson 7, Fundamentals of Fluid Flow Lesson 8, Flow in Closed Conduits Lesson 9 Complex Pipeline Systems Lesson 9, Complex Pipeline Systems Lesson 10, Flow in Open Channels Lesson 11, Flow of Compressible Fluids Lesson 12, Measurement of Flow of Fluids

l d b l d Lesson 13, Forces Developed by Moving Fluids Lesson 14, Fluid Machinery