Advertisements
Advertisements
प्रश्न
Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is p0.
Advertisements
उत्तर
Let p0 be the density of air on the surface of the earth.
As per the question, pressure ∝ density
⇒ `p/p_0 = ρ/ρ_0`
⇒ `ρ = ρ_0/p_0 p`
∴ `dp = - (ρ_0g)/p_0 pdh` ......[∵ dp = – ρgdh]
⇒ `(dp)/p = - (ρ_0g)/p_0 dh`
⇒ `int_(p_0)^p (dp)/p = - (ρ_0 g)/p_0 int_0^h dh` .....`[(∵ at h = p, r = p_0),(and at h = h, p = p)]`
⇒ In `p/ρ_0 = - (ρ_0 g)/p_0 h`
By removing log, `p = p_0e (- (ρ_0gh)/p_0)`
APPEARS IN
संबंधित प्रश्न
Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain.
A manometer reads the pressure of a gas in an enclosure as shown in Figure (a) When a pump removes some of the gas, the manometer reads as in Figure (b) The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.
(a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury.
(b) How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).
A satellite revolves round the earth. Air pressure inside the satellite is maintained at 76 cm of mercury. What will be the height of mercury column in a barometer tube 1 m long placed in the satellite?
The three vessels shown in the following figure have same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be
Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are ρA, ρB, ρC with ρA < ρB < ρC. The force on the base will be
Shows in the following figure a siphon. The liquid shown is water. The pressure difference PB − PAbetween the points A and B is
Suppose the pressure at the surface of mercury in a barometer tube is P1 and the pressure at the surface of mercury in the cup is P2.
A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will be ______.
A barometer kept in an elevator accelerating upward reads 76 cm. The air pressure in the elevator is
The surface of water in a water tank on the top of a house is 4 m above the tap level. Find the pressure of water at the tap when the tap is closed. Is it necessary to specify that the tap is closed?
The area of cross section of the wider tube shown in figure is 900 cm2. If the boy standing on the piston weighs 45 kg, find the difference in the levels of water in the two tubes.
A closed vessel is half filled with water. There is a hole near the top of the vessel and air is pumped out from this hole.
(a) The water level will rise up in the vessel.
(b) The pressure at the surface of the water will decrease
(c) The force by the water on the bottom of the vessel will decrease
(d) The density of the liquid will decrease
If water be used to construct a barometer, what would be the height of water column at standard atmospheric pressure (76 cm of mercury) ?
Water is filled in a rectangular tank of size 3 m × 2 m × 1 m. (a) Find the total force exerted by the water on the bottom surface on the tank. (b) Consider a vertical side of area 2 m × 1 m. Take a horizontal strip of width δx metre in this side, situated at a depth of x metre from the surface of water. Find the force by the water on this strip. (c) Find the torque of the force calculate in part (b) about the bottom edge of this side.
(d) Find the total force by the water on this side.
(e) Find the total torque by the water on the side about the bottom edge. Neglect the atmospheric pressure and take g = 10 ms−2.
A U-tube containing a liquid is accelerated horizontally with a constant acceleration a0. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.
Water leaks out from an open tank through a hole of area 2 mm2 in the bottom. Suppose water is filled up to a height of 80 cm and the area of cross section of the tanks is 0.4 m2. The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank. (a) Find the initial speed of water coming out of the hole. (b) Find the speed of water coming out when half of water has leaked out. (c) Find the volume of eater leaked out using a time interval dt after the height remained is h. Thus find the decrease in height dh in terms of h and dt.
(d) From the result of park (c) find the time required for half of the water to leak out.
