The water of a 14’ × 48’ metal frame pool can drain from the pool through an opening at the side of the pool. The opening is about h = 1.11 m below the water level. The capacity of the pool is V = 3880 gallons, the pool can be drained in t = 10.2 mins. P0 is the pressure of the atmosphere. ρ is the density of the water. a) Write the Bernoulli’s equation of the water at the top of the pool in terms of P0, ρ, h. Assuming the opening is the origin. b) Write the Bernoulli’s equation of the water at the opening of the pool in terms of P0, ρ, h and v, where v is the speed at which the water leaves the opening. Assuming the opening is the origin. c) Express the flow rate of the water in terms of V and t. d) Calculate the numerical value of A in cm2
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
The water of a 14’ × 48’ metal frame pool can drain from the pool through an opening at the side of the pool. The opening is about h = 1.11 m below the water level. The capacity of the pool is V = 3880 gallons, the pool can be drained in t = 10.2 mins. P0 is the pressure of the atmosphere. ρ is the density of the water.
a) Write the Bernoulli’s equation of the water at the top of the pool in terms of P0, ρ, h. Assuming the opening is the origin.
b) Write the Bernoulli’s equation of the water at the opening of the pool in terms of P0, ρ, h and v, where v is the speed at which the water leaves the opening. Assuming the opening is the origin.
c) Express the flow rate of the water in terms of V and t.
d) Calculate the numerical value of A in cm2
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