A reservoir discharging water through sluices at a depth hbelow the water surface area Afor various values has given below: hft1011121314( . .)Asqft9501070120013501530If tdenotes time in minutes, the rate of fall of the surface is given by 48dhhAdtEstimate the time taken for the water level to fall from 14 to 10 ft. above the sluices.

An insulated, electrically-heated (100 kW) tank contains400 kg of water at 65°C when its power is lost. Water iswithdrawn at a steady rate of 0.4 kg/s and cold water (at12°C) enters the tank at the same rate. Assume the tankis well-mixed, and neglect heat gains or losses throughthe tank walls.  For the water, c=cp=cv=4200 J/kg C(a) Create a script (m-file) in MATLAB to calculate howlong will it take for the tank’s temperature to fall to 25°C.(b) Display the entire program code used for your scriptcreated in MATLAB. Make sure that running the scriptprovides a numeric result and include your name as acomment.

answer in matlab script. do not use ai to solve.

Discuss on the need for numerical approximation of solutions to different equations.

SITUATION 1 (Fluid Flow in a Closed Conduit) Consider a fluid, with density (p) of 998.21 kg/m³ and dynamic viscosity (u) of 1.002 x 103 N-s/m², flowing in a 2000-meter long, 50-mm diameter smooth round pipe with velocity of 2.5 m/s. The energy loss on the pipe flow (he) due to friction between the pipe and the fluid is determined using Darcy-Weisbach equation, given as h₁ = f (²) (1/1) where f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of the flow, and g is the gravitational acceleration. The friction factor may be determined using an empirical equation developed by Nikuradse for flow in smooth pipes, given as 1 =0.869 In (Re√7)-0.8 where Re is the Reynolds number of the flow, determined as VDp R₂ = μl The friction factor equation given is only valid for flows with Reynolds number higher than 4000 (turbulent flow). Guide Questions: Determine the Reynolds number of the flow. Is the Nikuradse equation for friction factor…