An electric motor drives a pump that lifts water from a well that is 11.9 m deep and then delivers the water through a hose at a rate of 180 L/min and a speed of 21.0 m/s.If we assume 100% efficiency and ignore viscosity,the current drawn by the motor from a 220-V source is

Question

Quizplus · Accepted Answer

To calculate the current drawn by the motor, we first need to determine the power required to lift the water and then deliver it through the hose at the given speed. The power required for lifting the water (P1) can be calculated using the formula for gravitational potential energy, which is P = mgh/t, where m is the mass flow rate, g is the acceleration due to gravity (9.8 m/s^2), h is the height (11.9 m), and t is the time. The mass flow rate (m) can be found from the volume flow rate (180 L/min or 0.18 m^3/min) and the density of water (1000 kg/m^3). The power required to deliver the water at the given speed (P2) can be calculated using the kinetic energy formula, which is P = 0.5 * m * v^2 / t, where v is the velocity (21.0 m/s). However, since the question assumes 100% efficiency and ignores viscosity, we only need to consider the power for lifting the water, as the delivery speed is not relevant to the power calculation due to these assumptions. Therefore, the total power required is just for lifting the water, and once we calculate that, we can find the current using the formula P = VI, where V is the voltage (220 V) and I is the current. Rearranging this formula gives us I = P/V. Calculating the power for lifting the water and then dividing by the voltage gives us the current, which matches the value for choice A.

An Electric Motor Drives a Pump That Lifts Water from a Well