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Water flows over section of Niagara Falls at a rate of 1.20 106 kg/s and falls 50.0 m. What is the power of the waterfall?294 Mw588 MW60.0 Mw147 MW...

Question

Water flows over section of Niagara Falls at a rate of 1.20 106 kg/s and falls 50.0 m. What is the power of the waterfall?294 Mw588 MW60.0 Mw147 MW

Water flows over section of Niagara Falls at a rate of 1.20 106 kg/s and falls 50.0 m. What is the power of the waterfall? 294 Mw 588 MW 60.0 Mw 147 MW



Answers

Water flows over a section of Niagara Falls at the rate of $1.2 \times 10^{6} \mathrm{kg} / \mathrm{s}$ and falls $50.0 \mathrm{m} .$ How much power is generated by the falling water?

Question number 36 We know that power is equal to energy upon time Here, the falling border has kind of take energy. This is equal Toda initial gravitational potential energy so we can write energy is equal to mg etch they were dead by time. This is equal to power now substituting the values in it B is equal to Maher says 1.2 indoor 10 to the power six in the nine point it in tow 50 they were dead by one I'm is one second solving this We will get a power as five point it a Indo 10 to the power it But this is the required by one.

Susan. Given the rate of the falling off water, Alexa Thio Yes, they are. That is equals to 1.2. Living out of six kg per second height is given in the vehicle to 50 m. So basically we have to help with the powers related because of the changing gravitational potential. Energy. So so the power generator t will be nothing but RG at and that will be aren't here actually. So that would be nothing but from point to Internet ground of six into 9.8 into 50 then that come out something around 5.88 The gender gap off June 2nd. The power is the extra energy which lately ingredients simpleton water of the water.

As we know, power is equals two plugged in person worked in paree No time. The work done here is MD at. That is potential energy wherever time to compete. The mosque can be written as volume multiplied by density. So it will be row multiplied by density. Gs. They arose, their density and V. Is the volume. Whatever time taken for now the density of the water. Let's pull the density of water is 1000. Is he permitted? You multiplied with volume florid. Mm. He's given us 550 million m Cuba of Water. Permanent. Uh That's right. 550 Multiplied. Wait 10-4 of six meter cube of water per minute divided where 60 seconds multiplied with G, which is 9.8 m/s square. Multiplied with heads. It even is 100 m. After solving, we will get power is equals two eight point I mean 83 And spread with 10 to the power will work. So this is the required power For the total power in the water pool. 8.983 mold paired with 10-12 boards

Yeah. All right. So, we've got the rate of volume of water that is passing over this waterfall of 73,800 m3 per minute. But we're also told the density of water is 1000 kg per cubic meter. And so we can use that to figure out the rate of mass going over the waterfall. So that's going to be just 1000 times the rate for volume. And so we get 7.38 times to seven kg per minute. All right, Converting that into kg per second. We get 1.23 times 10 to the 6th kg of water every second. Now, the power is the rate of change in energy per unit time. And since we have this water falling, it's gonna gain kinetic energy as it falls. And that's going to be equal to the change in its potential energy. So, MG delta H. And the height is that 96.3 m. The key thing here though is that M over tea is what we have right up here. The rate of mass per unit time is M over T. So, we're going to use that M over tee times G times delta H. Where delta H is 96.3 meters. And we'll get a total power output available As 1.16 times 10 to the 9th. Watts. But unfortunately, our damn only can convert 58% of that into usable power. So we're only going to get uh 6.73 times 10 to the eighth watts. So you just take The total power and times it by 0.58 to get this value right here.


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