show work please A large tank of water has a horse connected to it, as shown in

Question

show work please

A large tank of water has a horse connected to it, as shown in the figure (Figure 1). The tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the value 3. 50 m, the absolute pressure p of the compressed air is 4.20 times 10 Pa. Assumed that the air above the water expands at constant tempeature, a take the atmospheric pressure to be 1.00 times 105 Pa. As water flows out of the tank, h decreases. Calculate the speed of flow for h= 2.90m. Calculate the speed of flow for h=2.10m. At what value of h does the flow stop?

Explanation / Answer

use bernoulli's principle:

P1+d1*g*h1+0.5*d1*v1^2=P2+d2*g*h2+0.5*d2*v2^2

where P1,P2 are pressure values

d1,d2 are density values

v1,v2 are speeds

h1,h2 are heights

part B:

as temperature remains constant,PV=constant

so as h changes,pressure also changes.

volume=cross section area*(4-h)

so 4.2*10^5*(4-3.5)=P1*(4-h1)

hence at h1=2.9 m,

pressure will be

P1=1.91*10^5 Pa.

h1=2.9 m

d1=d2=1000 kg/m^3

v1=0

h2=1 m

P2=1*10^5 Pa

putting the values

we get v2=14.8 m/s

part C:

at h=2.1 m,

P1=1.105*10^5 Pa.

h1=2.1 m

h2=1 m

v1=0

we get v2=6.527 m/s

Part d:

for v2=0,

let height be h.

then 2.5*10^5/(4-h) +10^3*9.8*(h-1)-10^5=0

2.5*10^5+9.8*10^3*(h-1)*(4-h)-10^5*(4-h)=0

h=1.39 m

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