water is pump from lake by an engine at a height of 5m above the lake surface.

if the water is discharged through a nozzle of radius 7cm with speed of 33m/s calculate the power needed asumming perfect energy conversation in the system.
density of water = 1g/cm^2.
acceleration 10m/s/?

find the volume of water per second

... a cylinder with a 7 cm diameter and a 33 m length
... convert to mass of water

find energy (work) ... work = m g h

work / time = power ... Joules / sec = watts

To calculate the power needed by the engine to pump the water from the lake, we first need to determine the kinetic energy of the water being discharged through the nozzle.

The kinetic energy (KE) of an object can be calculated using the formula:
KE = 0.5 * m * v^2

Where:
KE is the kinetic energy
m is the mass of the object
v is the velocity of the object

To find the mass of the water being discharged, we need to calculate its volume first. The volume of water flowing out per second can be determined using the formula:
Q = A * v

Where:
Q is the volume flow rate
A is the cross-sectional area of the nozzle
v is the velocity of water flowing out

The cross-sectional area of the nozzle can be calculated using the formula:
A = π * r^2

Where:
A is the cross-sectional area
π is a constant (approximately 3.14)
r is the radius of the nozzle

We are given the radius of the nozzle as 7 cm. Let's convert it to meters:
r = 7 cm = 0.07 m

Now we can calculate the cross-sectional area:
A = π * (0.07 m)^2

Next, we are given the velocity of the water flowing out as 33 m/s.

Using the volume flow rate and density, we can calculate the mass flow rate (m_dot) of water:
m_dot = Q * ρ

Where:
m_dot is the mass flow rate
Q is the volume flow rate
ρ is the density of water

We are given the density of water as 1 g/cm^3. Let's convert it to kg/m^3:
ρ = 1 g/cm^3 = 1000 kg/m^3

Now we can calculate the mass flow rate:
m_dot = Q * ρ

Finally, we can calculate the kinetic energy (KE) of the water being discharged:
KE = 0.5 * m_dot * v^2

The power (P) required can be obtained by dividing KE by time (t):
P = KE / t

However, we are not given the time it takes for the water to be discharged, so we cannot calculate the power needed without that information.