A vertical gate, hinged to a structure at its top, is impacted by a jet of fluid as shown below. The jet impacts the gate $10$ ft from its bottom. The gate is held closed by a block on the bottom of its left side. The gate is $40$ ft long $(L1=40ft)$ and $8$ ft wide.

The jet of fluid has an area of Ajet$=0\mathrm{.}19f{t}^2$ and is produced by a pump that pumps an unknown fluid from a large tank with a depth, d $,$ of $20$ ft $.$ The unknown fluid flows from the tank through a pipe with a total length of $100$ feet, a diameter of $6$ in $,$ and a friction factor of $0\mathrm{.}015.$ The pipe includes a sharp entrance $(K=0\mathrm{.}5)$ and all elbows are $90$ flanged elbows $(K=1\mathrm{.}2).$ The lengths of the sections of pipe shown below are: $L2=15ft,L3=10ft,L4=8ft,L5=14ft.$

The manometer attached to the large tank contains a gage fluid with $SG=0\mathrm{.}7$ and has readings as follows: $h1=4in,h2=3in,h3=3in,h4=14in,$ and $h5=5in.$

a$)$ What is the specific weight of the unknown fluid in the tank?

b$)$ Assuming the unknown fluid is water, what is the power required by the pump to produce a jet with a velocity of $14f\frac{t}{s}?$

c$)$ What is the force required by the block to hold the gate closed as shown below, assuming the jet has a velocity of $14f\frac{t}{s}?$

Start with the general form of any equations used and state why$/$how terms are simplified. State any assumptions you make, and mark on the sketch any reference points you use to solve this problem. Show all of your work, and include correct units in the final answer. Note: you do not need to re$-$sketch the figure in your solution, but you do need to sketch an appropriate FBD and a CV$.$