Lecture 14.2 Fluids II

HW #13 (Chapter 14) Read Sections 14-1 to 14.5 Problems: 14.4, 14.26, 14.35, 14.39, Due: Thursday May 8

Ideas From Last Thursday Density is a material property  = mas/volume Pressure is force/area (unit Pascal = 1 N/m 2 ) Fluids transfer pressure Example: hydraulic lift Pressure increases as you go down in a fluid P = P 0 +  gh Buoyancy is an upward force equal to the weight of the displaced fluid

New Ideas for Today Equation of Continuity Bernoulli’s Equation Maybe thought on waves Quiz

Pascal’s Law Pressure is the same at the height in a fluid F 1 /A 1 = F 2 /A 2

Slightly harder Buoyancy problem A raft consists of a block of wood (p = 0.7 x 10 3 kg/m 3 ) that is 2.0 m by 2.0 m by 0.5 m. How many 100 kg people will fit on the raft before it sinks? Steps: 1) Physical Diagram 2) Free body diagram 3) Equation that balances forces 4) Solve

A block of ice (density 920 kg/m 3 ) and a block of iron (density 7800 kg/m 3 ) are both submerged in a fluid. Both blocks have the same volume. Which block experiences the greater buoyant force? A. the block of ice B. the block of iron C. Both experience the same buoyant force. D. The answer depends on the density of the fluid. Q14.2 Concept Question

Fluid flow

Fluid flow II: Equation of Continuity The incompressibility of fluids allows calculations to be made even as pipes change. A 1 v 1 = A 2 v 2

Bernoulli’s equation Equation allows us to calculate the effect of fluid flow on pressure Other things being equal: As velocity goes up pressure goes down!

The Venturi meter

A. 4 times the fluid speed. B. 2 times the fluid speed. C. the same fluid speed. D. 1/2 the fluid speed. E. 1/4 the fluid speed. Q14.5 An incompressible fluid flows through a pipe of varying radius (shown in cross-section). Compared to the fluid at point P, the fluid at point Q has radius 2R radius R PQ Equation of Continuity

An incompressible fluid flows through a pipe of varying radius (shown in cross-section). Compared to the fluid at point P, the fluid at point Q has A. greater pressure and greater volume flow rate. B. greater pressure and the same volume flow rate. C. the same pressure and greater volume flow rate. D. lower pressure and the same volume flow rate. E. none of the above Q14.4 radius 2R radius R PQ Bernoulli’s Principle

Bernoulli Problem (med) A large tower that is full of water consist of a cylinder that is 10 m high. It is open at the top. You drill two small holes in the tower, one half way up and a second near the bottom. Compare the speed of the water coming out each hole Steps: 1) draw system 2) locate points to apply Bernoulli’s equation 3) write equations 4) solve