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 = 1.03 m below the water level. the capacity of the pool is v = 3780 gallons, the pool can be drained in t = 13.5 mins. p0 is the pressure of the atmosphere. rho is the density of the water.

(a) write the bernoulli's equation of the water at the top of the pool in terms of p_0, rho, h. assuming the opening is the origin 0% deduction per feedback.
(b) write the bernoulli's equation of the water at the opening of the pool in terms of p_0, rho, h and v, where v is the speed at which the water leaves the opening. assuming the opening is the origin.
(c) express v^2 in terms of g and h.
(d) calculate the numerical value of v in meters per second.
(e) express the flow rate of the water in terms of v and t.
(f) express the cross-sectional area of the opening, a, in terms of v, v and t.
(g) calculate the numerical value of a in cm^2

Explanation:

Height h = 1.03m

Volume v = 3780 gallons = 3780 * 0.0037851m^3 = 14.3073m^3

Time t = 13.5 mins = 13.5 * 60 = 810 seconds

Length of pool L = 14 inch = 14 * 2.54 = 35.56cm

width of pool b = 48 inch = 48 * 2.54 = 121.92 cm

a.) Consider the bernoulli's equation is given as:

consider the equation of bernoulli at the top of the pool

where atm pressure

At the top of the pool , substitute in V_1 in equation (2)

Hence equation (3) serves as the bernoullis equation at the top.

b.) Consider the equation of bernoulli's at the opening of the pool

where atm pressure and

Hence equation (6) serves as the bernoullis equation of water at the opening of the pool.

c.) Consider the equation (3) and (4)

Hence velocity is

d.) consider (7)

This is the norminal value of velocity  

e.) consider the equation of flow rate interval of v and t

flow(t)= hence this is the flow rate

f.) Consider the equation cross sectional area in terms of V,v2 and t

hence this serves as the cross sectional area.

g.) Consider the equation of area from equation (8)

answer: 500 wph.

explanation:

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