Respuesta :
Answer:
The gauge pressure as calculated is 5862.36 Pa
Solution:
As per the question:
Radius, r = 1 cm = 0.01 m
Length, l = 60 cm = 0.6 m
Velocity of discharge of fluid from the mouth, v = 1.5 m/s
Now,
By using the continuity equation:
Av = A'v' (1)
where
A = Area of the mouth
A' = Area of the tube
v' = Velocity of the fluid inside the stomach
Since, the question assumes the stomach, mouth and esophagus as continuous vertical tube, then:
A = A'
Thus
From eqn (1):
v = v' = 1.5 m/s
Now,
With the help of Bernoulli's equation:
[tex]P + \frac{1}{2}\rho v^{2} + \rho gh = P' + \frac{1}{2}\rho v'^{2} + \rho gh'[/tex]
[tex]P + \frac{1}{2}\rho v^{2} + \rho g(h - h') = P' + \frac{1}{2}\rho v^{2} + [/tex]
[tex]\rho g(h - h') = P' - P[/tex]
where
h - h' = l = 60 am = 0.6 m
P = Pressure at mouth = 1 atm = [tex]1\times 10^{5}\ Pa[/tex]
g = acceleration due to gravity
Density of water, [tex]\rho = 997\ kg/m^{3}[/tex]
P' = Pressure inside the stomach
P' - P = Gauge Pressure
[tex]P' - P = 997\times 9.8\times 0.6 = 5862.36\ Pa[/tex]
