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Answer:

The power of the pump is 23.09 kW.

Explanation:

Parameters

gravitational constant,

mass flow rate,

flow density,

efficiency of the pump,

output gauge pressure,

input gauge pressure,

cross-sectional area of output pipe,

cross-sectional area of input pipe,

height of discharge, (evaluated at pump’s maximum height of 1.22 m)

input height,

hydraulic power of the pump,

Initially, the volumetric flow (Q) needs to be determined

Next, compute the velocity (v) for both input and output

Subsequently, the total head (H) can be calculated

Finally, the computation of pump power is done as follows

Answer:

Refer to the attached document

1512 ft

Explanation:

Because the acceleration is constant or zero, the acceleration-time graph consists of horizontal segments. The values for t2 and a4 are derived as follows:

Acceleration - Time

0 < t < 6: Velocity change = area beneath the a–t graph

V_6 - 0 =  (6 s)(4 ft/s²) = 24 ft/s

6 < t < t2: The velocity rises from 24 to 48 ft/s,

Velocity change = area beneath the a–t graph

48 - 24 = (t2 - 6) * 6

t2 = 10 s

t2 < t < 34: The velocity remains constant, meaning acceleration is zero.

34 < t < 40: Velocity change = area beneath the a–t graph

0 - 42 = 6*a4

a4 = - 8 ft / s²

A negative acceleration shows the area lies below the t-axis, indicating a decrease in speed.

Velocity - Time

Since acceleration remains constant or zero, the v−t graph is made up of linear segments connecting the calculated points.

Position change = area beneath the v−t graph

0 < t < 6:  x6 - 0 = 0.5*6*24 = 72 ft

6 < t < 10:    x10 - x6 = 0.5*4*(24 + 48) = 144 ft

10 < t < 34: x34 - x10 = 48*24 = 1152 ft

34 < t < 40: x40 - x34 = 0.5*6*48 = 144 ft

Summing these position changes yields the distance from A to B:

d = x40 - 0 = 1512 ft