Answer:
Flow-rate = 0.0025 m^3/s
Explanation:
We need to assume that the flow-rate of pure water entering the pond is the same as the flow-rate of brine leaving the pond, in other words, the volume of liquid in the pond stays constant at 20,000 m^3. Using the previous assumption we can calculate the flow rate entering or leaving the tank (they are the same) building a separable differential equation dQ/dt, where Q is the milligrams (mg) of salt in a given time t, to find a solution to our problem we build a differential equation as follow:
dQ/dt = -(Q/20,000)*r where r is the flow rate in m^3/s
what we pose with this equation is that the variable rate at which the salt leaves the pond (salt leaving over time) is equal to the concentration (amount of salt per unit of volume of liquid at a given time) times the constant rate at which the liquid leaves the tank, the minus sign in the equation is because this is the rate at which salt leaves the pond.
Rearranging the equation we get dQ/Q = -(r/20000) dt then integrating in both sides ∫dQ/Q = -∫(r/20000) dt and solving ln(Q) = -(r/20000)*t + C where C is a constant (initial value) result of solving the integrals. Please note that the integral of dQ/Q is ln(Q) and r/20000 is a constant, therefore, the integral of dt is t.
To find the initial value (C) we evaluate the integrated equation for t = 0, therefore, ln(Q) = C, because at time zero we have a concentration of 25000 mg/L = 250000000 mg/m^3 and Q is equal to the concentration of salt (mg/m^3) by the amount of liquid (always 20000 m^3) -> Q = 250000000 mg/m^3 * 20000 m^3 = 5*10^11 mg -> C = ln(5*10^11) = 26.9378. Now the equation is ln(Q) = -(r/20000)*t + 26.9378, the only thing missing is to find the constant flow rate (r) required to reduce the salt concentration in the pond to 500 mg/L = 500000 mg/m^3 within one year (equivalent to 31536000 seconds), to do so we need to find the Q we want in one year, that is Q = 500000 mg/m^3 * 20000 m^3 = 1*10^10 mg, therefore, ln(1*10^10) = -(r/20000)*31536000 + 26.9378 solving for r -> r = 0.002481 m^3/s that is approximately 0.0025 m^3/s.
Note:
- ln() refer to natural logarithm
- The amount of liquid in the tank never changes because the flow-rate-in is the same as the flow-rate-out
- When solving the differential equation we calculated the flow-rate-out and we were asked for the flow-rate-in but because they are the same we could solve the problem
- During the solving process, we always converted units to m^3 and seconds because we were asked to give the answer in m^3/seg
D i took this hope it helps
Answer:
hello some part of your question is missing below is the complete question
answer :
A) 162750 Ib.ft
B) - 64950 Ib.ft
Explanation:
Applying Muller-Breslau's law
we will make assumptions which include assuming an imaginary hinge at G
therefore the height of I.LD for B.M at G = ( 12 * 8 ) / 20 = 4.8
height of I.L.D at C = 2.4 ( calculated )
height of I.L.D at F = 1.5 ( calculated )
A) Determine Maximum positive moment produced at G
= [ (1/2 * 20 * 4.8 ) ( 600 + 300 ) ] + [ ( 25 * 4.8 * 10^3 ) ] - [ ( 1/2 *2.4*20 ) * 300 ] + [ (1/2 * 1.5 * 10 ) ( 600 + 300 ) ]
= 162750 Ib.ft
B) Determine the maximum negative moment produced at G
= [ ( 1/2 * 20 * 4.8 ) * 300 ] - [ ( 1/2 * 2.4 * 20 ) ( 600 + 300 ) ] - [ (2.5 * 10^3 * 2.4 ) ] + [ ( 1/2 * 1.5 * 10) * 300 ]
= - 64950 Ib.ft
Answer:
Check the explanation
Explanation:
beam span = 25 ft
dead load = 0.6 kip/ft
live load = 2.1 kip/ft
factored load = 1.2*0.6 +1.6*2.1=4.08 kip/ft
moment in beam = 4.08*252/8=318.75 kip-ft = 3825 kip-in
design strength =0.9* 50 = 45 ksi
plastic section modulus required = 3825/45=85 in3
Moment in beam in ASD = (0.6+2.1)*252/8 = 210.9 kip-ft
lighest W section from LRFD = W21x44
lightest W section from ASD = W21x44