A pump can raise 900 liters of water per minute to a height of 50 meters caculate the h.p.(metric) of the pump.
Wt. = 900Liters * 1oz/0.03Liters = 30,000 Ozs. = 1875 Lbs./min.
Mass = 1875Lbs * 0.454kg/Lb. = 851.25 kg./min.
P = M*g*d/t = 851.25/60s * 9.8 * 50 = 6952 J/s = 6952 Watts.
h.p. = 6952/746 = 9.32.
To calculate the horsepower (hp) of the pump, we first need to convert the units.
1 horsepower (hp) is equivalent to 75 kg·m/s or 75 kg·m^2/s^3.
Since we are working with metric units, we'll use the equation:
Power (P, in watts) = mass flow rate (m, in kg/s) x acceleration due to gravity (g, in m/s^2) x height (h, in meters)
To calculate the mass flow rate, we need to convert the volume flow rate (900 L/min) to kg/s.
1 liter of water is equivalent to 1 kilogram.
Therefore, the mass flow rate (m) can be calculated as follows:
m = (900 L/min) x (1 kg/L) / (60 s/min)
m = 15 kg/s
Now, let's calculate the power in watts:
P = (15 kg/s) x (9.8 m/s^2) x (50 m)
P = 7350 W
Finally, let's convert the power from watts to horsepower:
1 horsepower (hp) = 735 W
Therefore, the horsepower (metric) of the pump is:
P_metic = P / 735
P_metric = 7350 W / 735
P_metric = 10 hp (metric)
So, the pump has a power of 10 horsepower (metric).
To calculate the horsepower (hp) of the pump, we need to convert the given information into the metric horsepower unit.
Since we know that 1 horsepower is equal to 75 kilogram-meters per second (kg m/s), we can use this conversion factor.
First, let's calculate the work done by the pump to raise the water:
Work (Joules) = force (Newtons) × distance (meters)
Force (Newton) = mass (kilograms) × acceleration due to gravity (9.8 m/s²)
The mass of the water can be determined using its density. Assuming the density of water is 1000 kg/m³, we can calculate the mass of 900 liters of water:
Mass (kilograms) = volume (cubic meters) × density (kg/m³)
Volume (cubic meters) = 900 liters × 1 cubic meter / 1000 liters
Once we have the mass, we can calculate the force exerted by the pump:
Force (Newton) = Mass (kilograms) × 9.8 m/s²
Next, we can calculate the work done by the pump:
Work (Joules) = Force (Newton) × Distance (meters)
Since power is the rate at which work is done, we can calculate the power in terms of kilogram-meters per second (kg m/s):
Power (kilogram-meters per second) = Work (Joules) / Time (seconds)
Finally, we can convert the power from kilogram-meters per second (kg m/s) to metric horsepower (hp):
Horsepower (metric) = Power (kg m/s) / 75
By plugging in the given values for the flow rate and height, we can calculate the metric horsepower (hp) of the pump.