A cylindrical tank with length 5 ft and raduis of 3 ft is situated wit its axis horizontal. if a circular bottom hole with a radius of 1 in. is opened and the tank is initially half full of xylene, how long will it ake for the liquid to drain completely? PLEASE HELP

Start with Bernoulli's equation which relates dV/dt to pressure. Yes, you will have to know density of xylene. http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html

This didn't help me much bobpursley, I am just so confused.

Write an equation (based on Bernoulli's equation) for the volume flow rate in terms of the height of the water in the tank, which is proportional to pressure. That height y will be a function of the remaining volume, V.

Derive the equation dV/dt = f{y(V)}
where y is the height of water in the tank. To get the time to empty the tank, solve by separation of variables.

Integral of t = Integral of dV/f(V)

dV/dt = -(hole area)*(liquid velocity at opening)
liquid velocity at opening= sqrt(2gy)

it appears that the liquid density cancels out. You will need to express y in terms of V to do the integration. The integration might be messy. That is as far as I am going with this.

To determine the time it takes for the liquid to drain completely, we need to calculate the volume of the liquid and then divide it by the rate at which the liquid drains through the hole.

Step 1: Calculate the volume of the liquid in the tank
The volume of a cylinder can be determined using the formula: V = πr^2h. Since the tank is initially half full, the height (h) of the liquid will be half the length of the tank. Additionally, we need to use consistent units, so we'll convert the radius from feet to inches.

Given:
Length of the tank (L) = 5 ft
Radius of the tank (r) = 3 ft = 36 in.
Radius of the hole (r_hole) = 1 in.

Height of the liquid (h) = L/2 = 5 ft / 2 = 2.5 ft = 30 in.

Volume of liquid (V_liquid) = πr^2h = π(36^2)(30) cubic inches

Step 2: Determine the rate of drainage
The rate at which the liquid drains through the hole depends on the size of the hole. In this case, the radius of the hole (r_hole) is given as 1 inch.

To find the rate of drainage, we need to calculate the area of the circular hole.

Given:
Radius of the hole (r_hole) = 1 in.

Area of the hole (A_hole) = πr_hole^2 square inches

Step 3: Calculate the time it takes to drain completely
To calculate the time it takes for the liquid to drain completely, we divide the volume of the liquid by the rate of drainage.

Time (t) = V_liquid / A_hole

Substitute the values of V_liquid and A_hole to find the time.

Finally, evaluate the expression to get the time it takes to drain completely.

Please note that the units used should be consistent throughout the calculations.