A burette is a vertical, right circular cylinder that is open at the top and has

Question

A burette is a vertical, right circular cylinder that is open at the top and has a stopcock valve at the bottom to let fluid out. Assume that you have a burette that has an inner diameter of 1 cm and a height of 100 cm. A. Assume that you fill the burette with water to some height, h. What is the relation between h and the pressure at the base of the burette? B. What is the relation between volume of water in the burette and the pressure? C. How does this relation map onto the relation between charge and voltage on a capacitor? D. What is the hydraulic analogue of voltage? E. What is the hydraulic analogue of voltage? F. Suppose you open the stopcock fully. The fluid will drain out. Assume a constant diameter of the opening of the stopcock that provides a constant resistance, R. Derive an equation that describes the time course of draining the burette. G. Identify the time constant for the burette emptying.

Explanation / Answer

A)
P bottom = pTop + rho*g*h

pTop = 1*10^5 N/m^2
rho is density of water = 1000 Kg/m^3
g is acceleration due to gravity = 9.8 m/s^2

so,
P bottom = pTop + rho*g*h
P bottom = 1*10^5 + 1000*9.8*h
P bottom = 1*10^5 + 9800*h

B)
R = 1 cm = 0.01 m

Volume = Pi*R^2*h
V = pi*(0.01)^2 * h
V = 3.14*10^-4 * h
h = 3183*V

Put this value of h in eqn got in part A
P bottom = 1*10^5 + 9800*h
P bottom = 1*10^5 + 9800*3183*V
P bottom = 1*10^5 + 3.12*10^8 V
This is relation between P and V

C)
Q = C*E for caapcitor

If we consider Q as similar to volume , V and E as similar to P
The above relation can map.

D)
Pressure is avalogue to volatage

E)
Volume is analog to Charge

I am allowed to answer only 4 parts at a time

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