Water is pumped into a storage tank from a well delivering 15.0 gallons of water

Question

Water is pumped into a storage tank from a well delivering 15.0 gallons of water in 30.0 seconds through a pipe of 1.00 in.2 cross-sectional area. What is the average velocity of the water in the pipe as the water is pumped from the well?
     in/s

A liquid (? = 1.65 g/cm3) flows through two horizontal sections of tubing joined end to end. In the first section the cross-sectional area is 10.0 cm2, the flow speed is 255 cm/s, and the pressure is 1.20 ? 105 Pa. In the second section the cross-sectional area is 3.50 cm2.

Explanation / Answer

gallons in litre = 56.78 litre = .056 m^3 in 30 sec so in 1 sec

volume = 1.8*10^-3 m^3/sec

velocity = Q/A = 1.8*10^-3/6.45*10^-4 = 2.79 m/sec

2) 10*255 = 3.5*v

v = 728.57cm/sec = 7.28m/sec

now apply bernaullis equation:

P1/p + v1^2/2 = P2/p + v2^2/2

P2 = .81*10^5 Pa

3) 1.6*10^-4 = A1*v1 = A2*v2

larger portion dia = 2.70cm

A1 = 5.72*10^-4 m^2

v1 = .279 m/sec

pressure, P1 = pgh1 = 980Pa

P2 = 490Pa

P1/p + v1^2/2 = P2/p + v2^2/2

v2 = 1.028 m/sec

so,

A2 = 1.55*10^-4

dia = .014 m

4) torque from centre = F*r = 5.38Nm

5) radius of 2.05 cm and a length of 11.5 cm

density = 10.49 g/cm^-3

volume = 37.93

mass = 397.97 g = .397 kg

moment of inertia = mr^2 = 1.59 *10^-4

6) A wheel of radius 6.65 cm turns with a constant angular speed of 6.27 revolutions per minute. The linear speed of a point on the rim of the wheel is

v = r*w
v = .043 m/sec

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