1- a pipe of diamter 1cm carreiers water flowing at 1m/s. the end of the pipe is bplugged and there is a small holeon the top as shown which is 1mm diameter. How high does the water go?
*=hole
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2. you're indoors, with a door 1m wide and 2.5m high. the wind blows past the door at 1 m /s. what is the net force on the door and its direction? the density of air is 1.2kh/m^3.
You look at a faucent and notice that the strema narrows as it falls. Suppose that the initial water speed is v1 and the initial area of the water faucent opening is A1. Findd the area of the water stream when it has fallen a distance H. The density of water is 1kg/liter and 1 liter is a volume of a cuber w. sides 0.1m.
4- a balooon filled w. helium (density 0.1785 g/L) see previous question for desnity of air and what a liter is). Assuming a baloon of radius 10cm and ignoring the mass of the baloon how much weight could the baloon lift?
You would get faster responses if you posted questions one at a time, and showed some of your work.
(1) Since the pipe is blocked at the end and the hole is 1/10 the pipe diameter, the velocity of the water leaving the hole must be 100 times a m/s, or 100 m/s. That seems very high to me. Get the height H by setting the kinetic energy leaving the hole equal to the potential energy increase at height H:
V = sqrt (2 g H)
Use the bernoulli equation to get the pressure differential bwtween the two sides of the door. The pressure will be lower on the outside where the wind is blowing by. The pressure difference is
(1/2) (density) V^2.
Multiply that by the door area for the force, which will be outward
1. To determine how high the water will go, you can use the concept of conservation of energy.
The kinetic energy of the water flowing in the pipe is given by: KE = (1/2)mv^2, where m is the mass of water and v is the velocity. Since the density of water is 1kg/L, the mass can be calculated as m = density * volume. The volume of water flowing per second can be obtained using the formula: volume = cross-sectional area * velocity.
Next, consider the potential energy gained by the water as it rises to a certain height H. The potential energy is given by PE = mgh, where g is the gravitational acceleration (9.8m/s^2) and h is the height.
Since the kinetic energy is equal to the potential energy (conservation of energy), we can equate the two expressions:
(1/2)mv^2 = mgh
Simplifying the equation and solving for h, you will have:
h = (v^2) / (2g)
Plug in the values given: v = 1m/s and g = 9.8m/s^2, and calculate the height h.
2. To determine the net force on the door, we need to consider the pressure difference between the inside and outside of the door due to the wind.
The pressure difference can be calculated using Bernoulli's equation: P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2, where P1 and P2 are the pressures on each side of the door, ρ is the density of air, and v1 and v2 are the velocities on each side.
Since the wind blows past the door, while the inside is relatively still, we can assume v1 = 0. The velocity on the outside is given as v2 = 1m/s.
Using the Bernoulli equation, we can rearrange it to solve for the pressure difference (P2 - P1) as:
P2 - P1 = (1/2)ρv2^2
Then, multiply the pressure difference by the area of the door to find the net force on the door.
3. The area of the water stream when it has fallen a distance H can be found using the conservation of mass.
The initial volume of water flowing per second can be calculated as volume = A1 * v1, where A1 is the initial area of the water faucet opening and v1 is the initial water speed.
The volume of water remains constant as it falls, so when it reaches a height H, the area can be calculated as A2 = volume / v2, where v2 is the speed of the water stream when it has fallen a distance H.
Plug in the known values: v1 (initial water speed), A1 (initial area), and v2 (speed when it has fallen a distance H), to calculate the area A2.
4. To calculate the weight the balloon can lift, we need to compare the buoyant force with the gravitational force.
The buoyant force on the balloon is given by the formula: F_buoyant = weight of displaced air = density of air * volume displaced * g, where g is the gravitational acceleration.
The volume displaced by the balloon can be calculated using the formula for the volume of a sphere: volume = (4/3) * π * r^3, where r is the radius of the balloon.
Since we are ignoring the mass of the balloon, the weight it can lift is equal to the buoyant force. Calculate the weight by plugging in the given values: density of air, radius of the balloon, and gravitational acceleration.