water is flowing through a 10 cm diameter hose on the first floor of a building

Question

water is flowing through a 10 cm diameter hose on the first floor of a building with a speed of 12 m/'s and an absolute pressure of 400 kpa the hose carries the water to the second story of the building and a height of 3.40 above its starting point where it exist the hose through a nozzle if a diameter 4.0 cm what is the speed of the water as it leaves the nozzle. what is the absolute pressure inside the nozzle.

12 points l An otyeet weghs 64 N when in air and 52 N when votenereed volume and density of the object. (12 points) water is flowing thraugh a 100 tm diameter hove em the fist fioor a speed of 12 m/s and an absolute pressure KPa second story of the building and a height of above its starting pont wher through a nozzle of diameter 40 cm. what is the speed of the water as t w What is the absolute pressure inside the nozzle?

Explanation / Answer

We solve this equation using the Bernoulli's equation in the Pressure head:

P1 +.5(rho)gh1 + .5(rho)v12 = P2 +.5(rho)gh2 + .5(rho)v22

(400000) + (.5x1000x9.8x0) + (.5x1000x144) = P2 + (.5x1000x9.8x3.4) + (.5x1000x(v2)2)

Since the difference in h is not too much at 3.4m height, it means the velocity remains constant v2 = 12m/s

(We make this assumption because 400 kPa = 4 bar pressure means water can reach roughly 4/.098 i.e. > 40m height and since 40 >> 3.4m we can go ahead with this assumption)

Thus, 400000 = 4900x3.4 + P2

P2 = 366.65 kPa (absolute pressure inside the nozzle)

Now, we use the continuity equation, A1V1 = A2V2

(pi*10*10)(12) = (pi*4*4)(V2) Thus, V2 = 75m/s

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