Water flows over a section of Niagara Falls at a rate of 1.2×106 kg/ s and falls 50m. How many 60W bulbs can be lit with this power?
And what efficiency do you assume for 1)the turbine, and 2) the electrical generator?
Let efficiency be E.
Power output= massflowrate*g*50m*E
Now, divide that by 60 to find the number of 60w bulbs.
To determine the number of 60W bulbs that can be lit with the given power, we need to calculate the total power consumption of the bulbs and then divide it by the power generated by the falling water.
First, let's find the total power consumption of the bulbs:
Total Power Consumption = Power per Bulb × Number of Bulbs
Since each bulb has a power rating of 60W, the total power consumption can be calculated by multiplying 60W by the number of bulbs. However, we don't know the number of bulbs yet, so we'll keep it as "N" for now.
Total Power Consumption = 60W × N
Next, we need to determine the power generated by the falling water:
Power Generated = Mass Flow Rate × Gravity × Height
Given that the mass flow rate is 1.2×10^6 kg/s and the height is 50m, the power generated can be calculated by multiplying the mass flow rate by the acceleration due to gravity (9.8 m/s^2) and the height.
Power Generated = 1.2×10^6 kg/s × 9.8 m/s^2 × 50 m
Now that we have both the total power consumption of the bulbs and the power generated by the falling water, we can set up an equation to find the number of bulbs (N):
Total Power Consumption = Power Generated
60W × N = 1.2×10^6 kg/s × 9.8 m/s^2 × 50 m
To solve for N, we can rearrange the equation:
N = (1.2×10^6 kg/s × 9.8 m/s^2 × 50 m) / 60W
Calculating this equation will give us the number of bulbs that can be lit with the given power generated by the falling water.
To determine the number of 60W bulbs that can be lit with the given power, we first need to calculate the total power available.
Power is equal to the product of mass flow rate and gravitational potential energy:
Power (P) = mass flow rate (m) * gravitational potential energy (h) * g
Where:
mass flow rate (m) = 1.2×10^6 kg/s (given)
gravitational potential energy (h) = 50 m (given)
g = 9.8 m/s^2 (acceleration due to gravity)
Substituting the given values, we have:
P = 1.2×10^6 kg/s * 50 m * 9.8 m/s^2
P = 5.88×10^8 W
Now, let's calculate the number of 60W bulbs that can be lit with this power:
Number of bulbs = Total power available / Power per bulb
Number of bulbs = 5.88×10^8 W / 60 W
Number of bulbs = 9.8×10^6 bulbs
Therefore, with the given power, approximately 9.8 million 60W bulbs can be lit.