Advertisements
Advertisements
प्रश्न
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?
उत्तर
Given:
Height of the water tank above the tap level, h = 4 m
Acceleration due to gravity, g = 10 m/s2
Density of water, ρ = 103 kg/m3
When the tap is closed, the pressure of the water in the tap is
P = hρg
On substituting the respective values in the formula, we get:
P = 4 × 103 × 10
= 40,000 N/m2
It is necessary to specify that the tap is closed because if the tap is open, then the pressure gradually decreases as h decreases and also because the pressure in the tap is atmospheric.
APPEARS IN
संबंधित प्रश्न
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).
During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. At what height must the blood container be placed so that blood may just enter the vein? [Use the density of whole blood from Table 10.1].
A barometer tube reads 76 cm of mercury. If the tube is gradually inclined keeping the open end immersed in the mercury reservoir, will the length of mercury column be 76 cm, more than 76 cm or less than 76 cm?
A one meter long glass tube is open at both ends. One end of the tube is dipped into a mercury cup, the tube is kept vertical and the air is pumped out of the tube by connecting the upper end to a suction pump. Can mercury be pulled up into the pump by this process?
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
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 ______.
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.
The weight of an empty balloon on a spring balance is W1. The weight becomes W2when the balloon is filled with air. Let the weight of the air itself be w. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon.
(a) W2 = W1
(b) W2 = W1 + w
(c) W2 < W1 + w
(d) W2 > W1
A glass full of water has a bottom of area 20 cm2, top of area 20 cm2, height 20 cm and volume half a litre.
(a) Find the force exerted by the water on the bottom.
(b) Considering the equilibrium of the water, find the resultant force exerted by the sides of the glass on the water. Atmospheric pressure = 1.0 × 105 N/m2. Density of water 1000 kg/m3 and g = 10 m/s2. Take all numbers
to be exact.
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.
Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh?
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.
