Chapter 5.6, Problem 23E

Transient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vt), can be expressed as: - Reservoir v(t) V2gh = tanh V2gh) Pipe Where h is the height of the fluid in the 7- reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh = tanh 2L 2gh water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < E

Speed is the derivative of the position function x = x (t) in relation to time t. What is the distance (in meters) that a bullet train travels in 4 seconds if it starts from position x = 0 m and its speed is given by v = 4t3 - 3t2 + 2t?    A) 336 m  B) 208 m  C) 216 m  D) 69,33 m  E) 212 m

1. A particle moves along the x-axis so that its velocity at any given time is = 2t - 3 and x (0) = 3. v(t) = a.) Find the equation for position of the particle as a function of t, x(t). b.) Find the position of the particle at t = 3. c.) At what values of t does the particle change direction? d.) Where is the particle when the position is a minimum?