Energy: Part 4. Water distribution. water tower. Bernoulli and Water distribution systems Physics 1010: Dr. Eleanor Hodby

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1 Energy: Part 4 ernoulli and Water distribution systems Physics 11: Dr. Eleanor odby Water distribution water tower reservoir pipe pump buildings Lecture 1: - Water distribution Reminders: W5 due Friday 1pm. Reading for Thursday: 9. Where does the water flow? What determines the water pressure in different homes/heights? ow fast does water flow out of a faucet? ow do you pump water out of wells? LL OUT CONSERVTION OF ENERGY! GPE = mgh. KE = ½ mv PPE = PV Pumps do work (Force x distance) (all of the physics of water distribution system) The super soaker (e.g. squirt guns) Pressure potential energy (PPE) What the heck is pressure anyway? Pressure = Force rea Pump up the pressure inside just a little bit and squirt. If we pump it up more, the water coming out will be: a. going slower than before, b. going the same speed, c. going faster. Units: 1Pascal (Pa) = 1N/m The plunger of a syringe has an area of 1cm. I push the plunger with a force of 5N. What s the pressure exerted by the plunger on the fluid inside? a) 5N/m b) 5 N/m c) 5N/m d) 5N/m e) 5N/m 5N Pressure potential energy (PPE) New form of potential energy for fluids PE is the energy of an object (or fluid) due to its CONDITION (situation, surroundings etc) Water of mass m, at height h has associated GPE = mgh because of its (vertical) position - work (mgh) was done to get the water from ground to that height - Physical details of how the work was done or how water is being supported is not important Water of volume V at pressure P has associated PPE = PV - Work (PV) was done to pressurize the water - Physical details of how the work was done or how the pressure is being maintained are not important Check that PV has units of energy (J) PV = N m 3 = Nm = J m 1. Pumping does work transforming chemical energy in my arm into PPE.. When I pull the trigger, pressure does work on the water. 3. When I fire upward, this KE turns into GPE Forms of energy in Super Soaker Pressure Pressure I apply a force, compress pump by a distance. Work = force X distance. Converts PPE into KE = ½ mv 1

2 Energy in a water distribution system The same three forms of energy exist in a water distribution system If we add up energy in these forms, the sum must be constant. It just sloshes back and forth between forms! PV + ½ mv + mgh = E total ernoulli s Equation ut what mass of water are we talking about, what height? PPE + KE + GPE = E total (constant) PV + ½ mv + mgh = E total Since E total is constant: If one thing changes, the other quantities must change correspondingly. - If pressure changes (water comes out of nozzle), v changes. - If height changes (go up in building), pressure or v changes, etc. Like the cart coasting up and down hills with no friction. Velocity and height are always connected If you know velocity and height at one place, can calculate it at all others. Consider one little bit of water of volume V and mass m: Replace m = rv where r is the fluid density PV + ½ rvv + rvgh = E total (r = mass/volume = 1kg/m 3 for water) We can divide through by V to get the standard form for ernoulli s equation: P + ½ rv + rgh = E total /V (E total per unit volume ) Just good old conservation of energy with the terms relabeled Since E total per vol is constant: Know P, v and h at one point can calculate these quantities at another pply ernoulli to Squirt Gun ow is velocity of water out related to pressure inside gun? More on pressure ere s a bucket of water with a faucet attached. What is the pressure at a depth? P inside v outside ernoulli s Equation: P + ½ rv + rgh = E tpv Compare water at surface and at depth P + ½ rv + rgh = E total per vol eight constant so ignore GPE P + ½ r v = E total per vol (constant) P? v = everywhere P + rgh = E tpv t surface: P = P, h = E tpv = P Inside gun: P = P + P pump, v= P + P pump = E total per vol t depth : P = P + P w, height = - Outside gun: P = P, v outside is big P + ½ r v outside = E total per vol E tpv = P + P w + rg(-) P + P pump = P + ½ r v outside P pump = ½ r v outside v outside = sqrt( P pump / r) E tpv constant P = P + P w rg P w = rg P = P + rg More on pressure ere s a bucket of water with a faucet attached. What is the pressure at a depth? tmospheric pressure P + rg ernoulli s Equation: P + ½ rv + rgh = E tpv Compare water at surface and at depth v = everywhere P + rgh = E tpv t surface: P = P, h = E tpv = P t depth : P = P + P w, height = - E tpv = P + P w + rg(-) E tpv constant P = P + P w rg P w = rg P = P + rg Pressure at surface of water = tmospheric pressure (P) 1, Pa Pressure due to air molecules hitting surface and exerting a force lways present at surface of earth Usually only interested in CNGES in water pressure and P cancels out If so can set zero of water pressure at P (like setting zero of height somewhere convenient) This pressure is exerted equally in all directions

3 With the faucet off, the water is stopped at point C. Rank the pressures at the three locations shown. Now open the faucet. What is the pressure at point C, just outside the faucet? a) P < P < P C b) P < P = P C c) P = P = P C d) P = P > P C a) tmospheric pressure b) The same as at c) Less than atmospheric pressure C C Consider a little bit of water leaving the faucet. What is its velocity at the faucet exit? (int: Question about pressure and velocity changes in fluid pply ernoulli s Eqn) a) Zero b) rg c) Sqrt(rg) d) g e) Sqrt (g) ernoulli s Equation in Real Life Total Energy per volume = P + ½ r v + rgh This is a good approximation but it cannot be perfectly correct What type of energy does it ignore? Think about a narrow pipe. Does not consider energy going into thermal energy- from friction with walls etc. For example, for high speed flow in a narrow pipe, more water molecules bounce off walls, creating significant friction and energy loss as heat ut for most water distribution systems, friction can be ignored E works very well. Water towers are everywhere! ut what exactly are they for? Water towers provide decent water pressure to buildings h h tower ow is height of tower (h tower ) and pressure at house related? E tpv = P + ½ r v + rgh 1. Consider water at top of tower: P =, v= and height = h tower E tpv = + + rgh tower r water = 1 kg/m 3 h=. Consider water at house: P = P house, v, and h = E tpv = P house + + Cons. of energy: E tpv = the same everywhere in system P house = rgh tower = (1)(9.8)h tower Strictly speaking, there is also one atmosphere of pressure at the top and at the bottom, but only the difference in pressure matters. 3

4 Water towers provide decent water pressure to buildings h h tower E tpv = P + ½ r v + rgh Cons. of energy: E tpv = the same everywhere in system P house = rgh tower = (1)(9.8)h tower What if the pipe from the water tower takes a weird path (say, over hills) to get to a house at the same height? r water = 1 kg/m 3 h= tmospheric pressure 1, Pa (= 14.6psi) bout how high would a water tower have to be to provide 1 atmosphere of water pressure to the house? a. m, b. 5 m c. 1 m d. m, e. 5 m. a) ouse has higher pressure b) ouse has higher pressure c) The pressure is the same at both houses. ere I have a tank of water with a hose connected to the bottom. When I take my finger off the hose, water (under pressure) will squirt into the air. Will the water go higher or lower than the opening in the tank (dashed line)? a. igher b. Right exactly to the dashed line c. Lower d. Impossible to predict e. None of the above. h ere I have a tank of water with a hose connected to the bottom. When I take my finger off the hose, water (under pressure) will squirt into the air. I can hold the hose high (at ) or low (at ). From which location will the water squirt higher (relative to the ground)? a., the higher location b., the lower location c. Water reaches the same height from both locations d. Impossible to predict e. None of the above. h h h t, the hose is.5 m below the water s surface. t it is 1. m below. ow much faster will the water come out at than at? a. ¼ as fast at as at. b. ½ as fast at as at c. same speed d. times faster at than at e. 4 times faster at than at h h h? What I I hold end of hose above the level of the water in tank? a. No water comes out b. Water comes out slowly c. Water comes out quickly d. Depends on shape of hose between tank and nozzle 4

5 Water distribution in skyscrapers The skyscraper water problem: Less pressure on the higher floors, Water won t make it to the top floor. E tpv = GPE here ow can you solve this problem? Put very high pressure pump at bottom (give water enough PPE at bottom) Use a series of pumps up the building Pump water to a tank on the roof, then you will always have some pressure on the floors below. 5

Static Fluids. **All simulations and videos required for this package can be found on my website, here:

Static Fluids. **All simulations and videos required for this package can be found on my website, here: DP Physics HL Static Fluids **All simulations and videos required for this package can be found on my website, here: http://ismackinsey.weebly.com/fluids-hl.html Fluids are substances that can flow, so